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<button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2411.15578">arXiv:2411.15578</a> <span> [<a href="https://arxiv.org/pdf/2411.15578">pdf</a>, <a href="https://arxiv.org/ps/2411.15578">ps</a>, <a href="https://arxiv.org/format/2411.15578">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Functions of continuous Ces谩ro operators </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A">Adolf Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2411.15578v1-abstract-short" style="display: inline;"> We describe holomorphic functions and fractional powers of Ces谩ro operators in $L^2(\mathbb{R})$, $L^2(\mathbb{R}_+)$, and $L^2[0,1]$. Logarithms of Ces谩ro operators are introduced as well and their spectral properties are studied. Several examples are considered. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2411.15578v1-abstract-full" style="display: none;"> We describe holomorphic functions and fractional powers of Ces谩ro operators in $L^2(\mathbb{R})$, $L^2(\mathbb{R}_+)$, and $L^2[0,1]$. Logarithms of Ces谩ro operators are introduced as well and their spectral properties are studied. Several examples are considered. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2411.15578v1-abstract-full').style.display = 'none'; document.getElementById('2411.15578v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 November, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47G10 (Primary) 45P05; 47B15; 47B38 (Secondary) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2406.10668">arXiv:2406.10668</a> <span> [<a href="https://arxiv.org/pdf/2406.10668">pdf</a>, <a href="https://arxiv.org/ps/2406.10668">ps</a>, <a href="https://arxiv.org/format/2406.10668">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> On boundedness of Hausdorff-type operators on Sobolev spaces </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2406.10668v1-abstract-short" style="display: inline;"> A new notion of a Hausdorff-type operator on function spaces over domains in Euclidean spaces is introduced, and a sufficient condition for the boundedness of this operator on Sobolev spaces is proved. It is shown that this condition cannot be weakened in general. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2406.10668v1-abstract-full" style="display: none;"> A new notion of a Hausdorff-type operator on function spaces over domains in Euclidean spaces is introduced, and a sufficient condition for the boundedness of this operator on Sobolev spaces is proved. It is shown that this condition cannot be weakened in general. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2406.10668v1-abstract-full').style.display = 'none'; document.getElementById('2406.10668v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 June, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 44A05; 44A30; 42B35; 47G10 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2312.09229">arXiv:2312.09229</a> <span> [<a href="https://arxiv.org/pdf/2312.09229">pdf</a>, <a href="https://arxiv.org/ps/2312.09229">ps</a>, <a href="https://arxiv.org/format/2312.09229">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Criteria for Analyticity of Multidimensionally Subordinate Semigroups </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2312.09229v1-abstract-short" style="display: inline;"> Let $蠄$ be a Bernstein function in one variable. A.~Carasso and T.~Kato obtained necessary and sufficient conditions for $蠄$ to have a property that $蠄(A)$ generates a quasibounded holomorphic semigroup for every generator $A$ of a bounded $C_0$-semigroup in a Banach space and deduced necessary conditions as well. We generalize their results to the multidimensional case and also give sufficient co… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2312.09229v1-abstract-full').style.display = 'inline'; document.getElementById('2312.09229v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2312.09229v1-abstract-full" style="display: none;"> Let $蠄$ be a Bernstein function in one variable. A.~Carasso and T.~Kato obtained necessary and sufficient conditions for $蠄$ to have a property that $蠄(A)$ generates a quasibounded holomorphic semigroup for every generator $A$ of a bounded $C_0$-semigroup in a Banach space and deduced necessary conditions as well. We generalize their results to the multidimensional case and also give sufficient conditions for the property mentioned above. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2312.09229v1-abstract-full').style.display = 'none'; document.getElementById('2312.09229v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 December, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47A60; 47D03 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2308.02388">arXiv:2308.02388</a> <span> [<a href="https://arxiv.org/pdf/2308.02388">pdf</a>, <a href="https://arxiv.org/ps/2308.02388">ps</a>, <a href="https://arxiv.org/format/2308.02388">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> On a general concept of a Hausdorff-type operator </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2308.02388v2-abstract-short" style="display: inline;"> A unified approach to the concept of a Hausdorff operator is proposed in such a way that a number of classical and new operators feet into the given definition. Conditions are given for the boundedness of the operators under consideration in $L^p$ and in the atomic Hardy space $H^1$, and their regularity property is investigated. Examples are considered. The author hopes that this approach will… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2308.02388v2-abstract-full').style.display = 'inline'; document.getElementById('2308.02388v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2308.02388v2-abstract-full" style="display: none;"> A unified approach to the concept of a Hausdorff operator is proposed in such a way that a number of classical and new operators feet into the given definition. Conditions are given for the boundedness of the operators under consideration in $L^p$ and in the atomic Hardy space $H^1$, and their regularity property is investigated. Examples are considered. The author hopes that this approach will allow one to unify the study of a lot of extensions and analogs of the classical Hausdorff operator. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2308.02388v2-abstract-full').style.display = 'none'; document.getElementById('2308.02388v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 June, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 4 August, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47B38 (Primary); 47B15; 46E30 (Secondary) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2307.03271">arXiv:2307.03271</a> <span> [<a href="https://arxiv.org/pdf/2307.03271">pdf</a>, <a href="https://arxiv.org/ps/2307.03271">ps</a>, <a href="https://arxiv.org/format/2307.03271">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> On the spectra of multidimensional normal discrete Hausdorff operators </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2307.03271v2-abstract-short" style="display: inline;"> In the paper the general case of a normal discrete Hausdorff operators in $L^2(\mathbb{R}^d)$ is considered. The main result states that under some natural arithmetic condition the spectrum of such an operator is rotationally invariant. Several special cases and examples are considered. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2307.03271v2-abstract-full" style="display: none;"> In the paper the general case of a normal discrete Hausdorff operators in $L^2(\mathbb{R}^d)$ is considered. The main result states that under some natural arithmetic condition the spectrum of such an operator is rotationally invariant. Several special cases and examples are considered. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2307.03271v2-abstract-full').style.display = 'none'; document.getElementById('2307.03271v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 11 July, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 6 July, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47B38 (Primary); 47B15; 47A10; 46E30 (Secondary) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2307.03255">arXiv:2307.03255</a> <span> [<a href="https://arxiv.org/pdf/2307.03255">pdf</a>, <a href="https://arxiv.org/ps/2307.03255">ps</a>, <a href="https://arxiv.org/format/2307.03255">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Analysis of PDEs">math.AP</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Some remarks on the solution of the cell growth equation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A">Adolf Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2307.03255v1-abstract-short" style="display: inline;"> The analytical solution to the initial-boundary value problem for the cell growth equation was given in the paper Zaidi A. A., Van Brunt B., Wake G.C., Solutions to an advanced functional partial differential equation of the pantograph type, Proc. R. Soc. A 471: 20140947 (2015). In this note, we simplify the arguments given in the paper mentioned above by using the theory of operator semigroups. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2307.03255v1-abstract-full" style="display: none;"> The analytical solution to the initial-boundary value problem for the cell growth equation was given in the paper Zaidi A. A., Van Brunt B., Wake G.C., Solutions to an advanced functional partial differential equation of the pantograph type, Proc. R. Soc. A 471: 20140947 (2015). In this note, we simplify the arguments given in the paper mentioned above by using the theory of operator semigroups. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2307.03255v1-abstract-full').style.display = 'none'; document.getElementById('2307.03255v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 6 July, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 35B40 (Primary) 35B41; 35L45; 92C17 (Secondary) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2306.14007">arXiv:2306.14007</a> <span> [<a href="https://arxiv.org/pdf/2306.14007">pdf</a>, <a href="https://arxiv.org/ps/2306.14007">ps</a>, <a href="https://arxiv.org/format/2306.14007">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> On the symbol calculus for multidimensional Hausdorff operators </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Liflyand%2C+E">E. Liflyand</a>, <a href="/search/math?searchtype=author&query=Mirotin%2C+A">A. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2306.14007v2-abstract-short" style="display: inline;"> The aim of this work is to derive a symbol calculus on $L^2(\mathbb{R}^n)$ for multidimensional Hausdorff operators. Two aspects of this activity result in two almost independent parts. While throughout the perturbation matrices are supposed to be self-adjoint and form a commuting family, in the second part they are additionally assumed to be positive definite. What relates these two parts is the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.14007v2-abstract-full').style.display = 'inline'; document.getElementById('2306.14007v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2306.14007v2-abstract-full" style="display: none;"> The aim of this work is to derive a symbol calculus on $L^2(\mathbb{R}^n)$ for multidimensional Hausdorff operators. Two aspects of this activity result in two almost independent parts. While throughout the perturbation matrices are supposed to be self-adjoint and form a commuting family, in the second part they are additionally assumed to be positive definite. What relates these two parts is the powerful method of diagonalization of a normal Hausdorff operator elaborated earlier by the second author. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.14007v2-abstract-full').style.display = 'none'; document.getElementById('2306.14007v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 July, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 24 June, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47B38 (Primary) 42B10 (Secondary) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2306.14000">arXiv:2306.14000</a> <span> [<a href="https://arxiv.org/pdf/2306.14000">pdf</a>, <a href="https://arxiv.org/ps/2306.14000">ps</a>, <a href="https://arxiv.org/format/2306.14000">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/s10958-023-06275-7">10.1007/s10958-023-06275-7 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Algebras of Hausdorff Operators on the Real Line </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Liflyand%2C+E">E. Liflyand</a>, <a href="/search/math?searchtype=author&query=Mirotin%2C+A">A. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2306.14000v1-abstract-short" style="display: inline;"> The aim of this work is to derive a symbol calculus on $L^2(\mathbb{R})$ for one-dimensional Hausdorff operators in apparently the most general form. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2306.14000v1-abstract-full" style="display: none;"> The aim of this work is to derive a symbol calculus on $L^2(\mathbb{R})$ for one-dimensional Hausdorff operators in apparently the most general form. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.14000v1-abstract-full').style.display = 'none'; document.getElementById('2306.14000v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 24 June, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 46B25 (Primary) 42A38; 30A99 (secondary) </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Journal of Mathematical Sciences (2023) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2208.06215">arXiv:2208.06215</a> <span> [<a href="https://arxiv.org/pdf/2208.06215">pdf</a>, <a href="https://arxiv.org/ps/2208.06215">ps</a>, <a href="https://arxiv.org/format/2208.06215">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> $渭$-Hankel Operators on Compact Abelian Groups </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2208.06215v1-abstract-short" style="display: inline;"> $(渭;谓)$-Hankel operators between separable Hilbert spaces were introduced and studied recently (\textit{$渭$-Hankel operators on Hilbert spaces}, Opuscula Math., \textbf{41} (2021), 881--899). This paper, is devoted to generalization of $(渭;谓)$-Hankel operators to the (non-separable in general) case of Hardy spaces over compact and connected Abelian groups. In this setting bounded $(渭;谓)$-Hankel op… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2208.06215v1-abstract-full').style.display = 'inline'; document.getElementById('2208.06215v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2208.06215v1-abstract-full" style="display: none;"> $(渭;谓)$-Hankel operators between separable Hilbert spaces were introduced and studied recently (\textit{$渭$-Hankel operators on Hilbert spaces}, Opuscula Math., \textbf{41} (2021), 881--899). This paper, is devoted to generalization of $(渭;谓)$-Hankel operators to the (non-separable in general) case of Hardy spaces over compact and connected Abelian groups. In this setting bounded $(渭;谓)$-Hankel operators are fully described under some natural conditions. Examples of integral operators are considered. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2208.06215v1-abstract-full').style.display = 'none'; document.getElementById('2208.06215v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 12 August, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47B35; 47A62; 47B90 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2201.09328">arXiv:2201.09328</a> <span> [<a href="https://arxiv.org/pdf/2201.09328">pdf</a>, <a href="https://arxiv.org/ps/2201.09328">ps</a>, <a href="https://arxiv.org/format/2201.09328">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Hausdorff Operators on Compact Abelian Groups </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2201.09328v1-abstract-short" style="display: inline;"> Necessary and sufficient conditions are given for boundedness of Hausdorff operators on generalized Hardy spaces $H^p_E(G)$, real Hardy space $H^1_{\mathbb{R}}(G)$, $BMO(G)$, and $BMOA(G)$ for compact Abelian group $G$. Surprisingly, these conditions turned out to be the same for all groups and spaces under consideration. Applications to Dirichlet series are given. The case of the space of continu… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2201.09328v1-abstract-full').style.display = 'inline'; document.getElementById('2201.09328v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2201.09328v1-abstract-full" style="display: none;"> Necessary and sufficient conditions are given for boundedness of Hausdorff operators on generalized Hardy spaces $H^p_E(G)$, real Hardy space $H^1_{\mathbb{R}}(G)$, $BMO(G)$, and $BMOA(G)$ for compact Abelian group $G$. Surprisingly, these conditions turned out to be the same for all groups and spaces under consideration. Applications to Dirichlet series are given. The case of the space of continuous functions on $G$ and examples are also considered. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2201.09328v1-abstract-full').style.display = 'none'; document.getElementById('2201.09328v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 January, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47B90 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2102.09859">arXiv:2102.09859</a> <span> [<a href="https://arxiv.org/pdf/2102.09859">pdf</a>, <a href="https://arxiv.org/ps/2102.09859">ps</a>, <a href="https://arxiv.org/format/2102.09859">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Boundedness of Hausdorff operators on Hardy spaces over homogeneous spaces of Lie groups </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2102.09859v1-abstract-short" style="display: inline;"> The aim of this note is to give the boundedness conditions for Hausdorff operators on Hardy spaces $H^{1}$ with the norm defined via $(1,q)$ atoms over homogeneous spaces of Lie groups with doubling property and to apply results we obtain to generalized Delsarte operators and to Hausdorff operators over multidimensional spheres. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2102.09859v1-abstract-full" style="display: none;"> The aim of this note is to give the boundedness conditions for Hausdorff operators on Hardy spaces $H^{1}$ with the norm defined via $(1,q)$ atoms over homogeneous spaces of Lie groups with doubling property and to apply results we obtain to generalized Delsarte operators and to Hausdorff operators over multidimensional spheres. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2102.09859v1-abstract-full').style.display = 'none'; document.getElementById('2102.09859v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 February, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">13 pages. arXiv admin note: text overlap with arXiv:2006.03281</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 43A85; 47G10; 22E30 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2101.05227">arXiv:2101.05227</a> <span> [<a href="https://arxiv.org/pdf/2101.05227">pdf</a>, <a href="https://arxiv.org/ps/2101.05227">ps</a>, <a href="https://arxiv.org/format/2101.05227">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Complex Variables">math.CV</span> </div> </div> <p class="title is-5 mathjax"> Hausdorff Operators on Some Spaces of Holomorphic Functions on the Unit Disc </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2101.05227v1-abstract-short" style="display: inline;"> We introduce Hausdorff operators over the unit disc and give conditions for boundedness of such operator in Bloch, Bergman, and Hardy spaces on the disc. Identity approximation by Hausdorff operators is also considered. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2101.05227v1-abstract-full" style="display: none;"> We introduce Hausdorff operators over the unit disc and give conditions for boundedness of such operator in Bloch, Bergman, and Hardy spaces on the disc. Identity approximation by Hausdorff operators is also considered. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2101.05227v1-abstract-full').style.display = 'none'; document.getElementById('2101.05227v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 January, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47G10; 47B38; 46E30 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2009.03685">arXiv:2009.03685</a> <span> [<a href="https://arxiv.org/pdf/2009.03685">pdf</a>, <a href="https://arxiv.org/ps/2009.03685">ps</a>, <a href="https://arxiv.org/format/2009.03685">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1134/S1061920820040081">10.1134/S1061920820040081 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> A Hausdorff Operator on Lebesgue Space With Commuting Perturbation Matrices Is a Non-Riesz Operator </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2009.03685v2-abstract-short" style="display: inline;"> We consider a generalization of Hausdorff operators on Lebesgue spaces and under natural conditions prove that such an operator is not a Riesz operator provided it is non-zero. In particular, it cannot be represented as a sum of a quasinilpotent and compact operators. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2009.03685v2-abstract-full" style="display: none;"> We consider a generalization of Hausdorff operators on Lebesgue spaces and under natural conditions prove that such an operator is not a Riesz operator provided it is non-zero. In particular, it cannot be represented as a sum of a quasinilpotent and compact operators. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2009.03685v2-abstract-full').style.display = 'none'; document.getElementById('2009.03685v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 November, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 6 September, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">arXiv admin note: text overlap with arXiv:2005.08003</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 45P05; 47G10; 47B06 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2007.10836">arXiv:2007.10836</a> <span> [<a href="https://arxiv.org/pdf/2007.10836">pdf</a>, <a href="https://arxiv.org/ps/2007.10836">ps</a>, <a href="https://arxiv.org/format/2007.10836">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> On the boundedness of Hausdorff operators on real Hardy spaces $H^1$ over homogeneous spaces of groups with local doubling property </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2007.10836v1-abstract-short" style="display: inline;"> We give conditions for boundedness of Hausdorff operators on real Hardy spaces $H^1$ over homogeneous spaces of locally compact groups with local doubling property. The special case of the hyperbolic plane is considered. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2007.10836v1-abstract-full" style="display: none;"> We give conditions for boundedness of Hausdorff operators on real Hardy spaces $H^1$ over homogeneous spaces of locally compact groups with local doubling property. The special case of the hyperbolic plane is considered. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2007.10836v1-abstract-full').style.display = 'none'; document.getElementById('2007.10836v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 July, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">arXiv admin note: text overlap with arXiv:2006.03281</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47G10; 43A85; 47A30; 51M10; 22E30 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2006.12474">arXiv:2006.12474</a> <span> [<a href="https://arxiv.org/pdf/2006.12474">pdf</a>, <a href="https://arxiv.org/ps/2006.12474">ps</a>, <a href="https://arxiv.org/format/2006.12474">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> On compact Hankel operators over compact Abelian groups </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2006.12474v1-abstract-short" style="display: inline;"> We consider compact and connected Abelian group $G$ with a linearly ordered dual. Based on the description of the structure of compact Hankel operators over $G$, generalizations of the classical Kronecker, Hartman, Peller and Adamyan-Arov-Krein theorems are obtained. A generalization of Burling's invariant subspace theorem is also established. Applications are given to Hankel operators over discre… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2006.12474v1-abstract-full').style.display = 'inline'; document.getElementById('2006.12474v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2006.12474v1-abstract-full" style="display: none;"> We consider compact and connected Abelian group $G$ with a linearly ordered dual. Based on the description of the structure of compact Hankel operators over $G$, generalizations of the classical Kronecker, Hartman, Peller and Adamyan-Arov-Krein theorems are obtained. A generalization of Burling's invariant subspace theorem is also established. Applications are given to Hankel operators over discrete groups <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2006.12474v1-abstract-full').style.display = 'none'; document.getElementById('2006.12474v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 June, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">In Russian (English Abstract)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 43A17; 47B35 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2006.03281">arXiv:2006.03281</a> <span> [<a href="https://arxiv.org/pdf/2006.03281">pdf</a>, <a href="https://arxiv.org/ps/2006.03281">ps</a>, <a href="https://arxiv.org/format/2006.03281">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> On Hausdorff operators on homogeneous spaces of locally compact groups </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2006.03281v2-abstract-short" style="display: inline;"> Hausdorff operators on the real line and multidimensional Euclidean spaces originated from some classical summation methods. Now it is an active research area. Hausdorff operators on general groups were defined and studied by the author since 2019. The purpose of this paper is to define and study Hausdorff operators on Lebesgue and real Hardy spaces over homogeneous spaces of locally compact group… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2006.03281v2-abstract-full').style.display = 'inline'; document.getElementById('2006.03281v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2006.03281v2-abstract-full" style="display: none;"> Hausdorff operators on the real line and multidimensional Euclidean spaces originated from some classical summation methods. Now it is an active research area. Hausdorff operators on general groups were defined and studied by the author since 2019. The purpose of this paper is to define and study Hausdorff operators on Lebesgue and real Hardy spaces over homogeneous spaces of locally compact groups. We introduce in particular an atomic Hardy space over homogeneous spaces of locally compact groups and obtain conditions for boundedness of Hausdorff operators on such spaces. Several corollaries are considered and unsolved problems are formulated. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2006.03281v2-abstract-full').style.display = 'none'; document.getElementById('2006.03281v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 August, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 5 June, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47G60; 43A85; 47A30; 26D15; 22E30 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2005.08003">arXiv:2005.08003</a> <span> [<a href="https://arxiv.org/pdf/2005.08003">pdf</a>, <a href="https://arxiv.org/ps/2005.08003">ps</a>, <a href="https://arxiv.org/format/2005.08003">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Hausdorff operators on Lebesgue spaces with positive definite perturbation matrices are non-Riesz </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2005.08003v1-abstract-short" style="display: inline;"> We consider generalized Hausdorff operators with positive definite and permutable perturbation matrices on Lebesgue spaces and prove that such operators are not Riesz operators provided they are non-zero. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2005.08003v1-abstract-full" style="display: none;"> We consider generalized Hausdorff operators with positive definite and permutable perturbation matrices on Lebesgue spaces and prove that such operators are not Riesz operators provided they are non-zero. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2005.08003v1-abstract-full').style.display = 'none'; document.getElementById('2005.08003v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 May, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 45P05; 47G10; 47B06 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1912.12423">arXiv:1912.12423</a> <span> [<a href="https://arxiv.org/pdf/1912.12423">pdf</a>, <a href="https://arxiv.org/ps/1912.12423">ps</a>, <a href="https://arxiv.org/format/1912.12423">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> On the connections of Hille-Phillips functional calculus with Bochner-Phillips functional calculus </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1912.12423v1-abstract-short" style="display: inline;"> The extension of Hille-Phillips functional calculus of semigroup generators which leads to unbounded operators is considered. Connections of this calculus to Bochner-Phillips functional calculus are indicated. In particular, the multiplication rule and the composition rule are proved. Several examples are given. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1912.12423v1-abstract-full" style="display: none;"> The extension of Hille-Phillips functional calculus of semigroup generators which leads to unbounded operators is considered. Connections of this calculus to Bochner-Phillips functional calculus are indicated. In particular, the multiplication rule and the composition rule are proved. Several examples are given. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1912.12423v1-abstract-full').style.display = 'none'; document.getElementById('1912.12423v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 28 December, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Russian, English summary</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47A60; 47D03 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1912.08105">arXiv:1912.08105</a> <span> [<a href="https://arxiv.org/pdf/1912.08105">pdf</a>, <a href="https://arxiv.org/ps/1912.08105">ps</a>, <a href="https://arxiv.org/format/1912.08105">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> The unbounded extension of Hille-Phillips functional calculus </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1912.08105v1-abstract-short" style="display: inline;"> The extension of Hille-Phillips functional calculus of semigroup generators which leads to unbounded operators is given. Connections of this calculus to Bochner-Phillips functional calculus are indicated, and several examples are considered. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1912.08105v1-abstract-full" style="display: none;"> The extension of Hille-Phillips functional calculus of semigroup generators which leads to unbounded operators is given. Connections of this calculus to Bochner-Phillips functional calculus are indicated, and several examples are considered. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1912.08105v1-abstract-full').style.display = 'none'; document.getElementById('1912.08105v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 17 December, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">In Russian, English abstract</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47A60; 47D03 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1912.03752">arXiv:1912.03752</a> <span> [<a href="https://arxiv.org/pdf/1912.03752">pdf</a>, <a href="https://arxiv.org/ps/1912.03752">ps</a>, <a href="https://arxiv.org/format/1912.03752">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> </div> </div> <p class="title is-5 mathjax"> On sums and products of periodic functions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a>, <a href="/search/math?searchtype=author&query=Mirotin%2C+E+A">E. A. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1912.03752v1-abstract-short" style="display: inline;"> The main purpose of this work is to ascertain when arithmetic operations with periodic functions whose domains may not coincide with the whole real line preserve periodicity. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1912.03752v1-abstract-full" style="display: none;"> The main purpose of this work is to ascertain when arithmetic operations with periodic functions whose domains may not coincide with the whole real line preserve periodicity. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1912.03752v1-abstract-full').style.display = 'none'; document.getElementById('1912.03752v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 8 December, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 26A </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1908.08029">arXiv:1908.08029</a> <span> [<a href="https://arxiv.org/pdf/1908.08029">pdf</a>, <a href="https://arxiv.org/ps/1908.08029">ps</a>, <a href="https://arxiv.org/format/1908.08029">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Analog for the Wiener Lemma for Wolff-Denjoy Series </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a>, <a href="/search/math?searchtype=author&query=Atvinovskii%2C+A+A">A. A. Atvinovskii</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1908.08029v2-abstract-short" style="display: inline;"> Let a function f with real poles be expanded in a Wolff-Denjoy series with positive coefficients. The main result of the note states that if we subtract its linear part from the function 1/f, then the remaining fractional part of this function will also expand into Wolff-Denjoy series (its poles are also real, and the coefficients of the series are negative). In other words, for Wolff-Denjoy serie… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1908.08029v2-abstract-full').style.display = 'inline'; document.getElementById('1908.08029v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1908.08029v2-abstract-full" style="display: none;"> Let a function f with real poles be expanded in a Wolff-Denjoy series with positive coefficients. The main result of the note states that if we subtract its linear part from the function 1/f, then the remaining fractional part of this function will also expand into Wolff-Denjoy series (its poles are also real, and the coefficients of the series are negative). In other words, for Wolff-Denjoy series of the indicated form, an analogue of the well-known Wiener lemma in the theory of Fourier series is true up to a linear term. Applications of the result to operator theory are given. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1908.08029v2-abstract-full').style.display = 'none'; document.getElementById('1908.08029v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 December, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 21 August, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">in Russian (English abstract)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 30D30; 47A60 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1908.02998">arXiv:1908.02998</a> <span> [<a href="https://arxiv.org/pdf/1908.02998">pdf</a>, <a href="https://arxiv.org/ps/1908.02998">ps</a>, <a href="https://arxiv.org/format/1908.02998">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Equations of the first kind and the inversion of series of resolvents of a closed operator </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1908.02998v2-abstract-short" style="display: inline;"> Let $A$ be a densely defined closed operator in a complex Banach space $X.$ Conditions for left invertibility of operators of the form $\sum_{j=1}^\infty a_j (伪_j -A)^{-1}$ are given. Several examples are considered. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1908.02998v2-abstract-full" style="display: none;"> Let $A$ be a densely defined closed operator in a complex Banach space $X.$ Conditions for left invertibility of operators of the form $\sum_{j=1}^\infty a_j (伪_j -A)^{-1}$ are given. Several examples are considered. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1908.02998v2-abstract-full').style.display = 'none'; document.getElementById('1908.02998v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 August, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 August, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">in Russian</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47A60; 47A20; 47A52; 45Q05 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1903.07096">arXiv:1903.07096</a> <span> [<a href="https://arxiv.org/pdf/1903.07096">pdf</a>, <a href="https://arxiv.org/ps/1903.07096">ps</a>, <a href="https://arxiv.org/format/1903.07096">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Fredholm and spectral properties of Toeplitz operators on $H^p$ spaces over ordered groups </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1903.07096v2-abstract-short" style="display: inline;"> Toeplitz operators on spaces $H^p(G)\ (1< p<\infty)$ associated with compact connected Abelian group $G$ with ordered dual are considered and the generalization of the classical Gohberg-Krein theorem on the Fredholm index of such operators with continuous symbols is proved. Applications to spectral theory of Toeplitz operators are given and examples of evident computation of index have been consid… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1903.07096v2-abstract-full').style.display = 'inline'; document.getElementById('1903.07096v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1903.07096v2-abstract-full" style="display: none;"> Toeplitz operators on spaces $H^p(G)\ (1< p<\infty)$ associated with compact connected Abelian group $G$ with ordered dual are considered and the generalization of the classical Gohberg-Krein theorem on the Fredholm index of such operators with continuous symbols is proved. Applications to spectral theory of Toeplitz operators are given and examples of evident computation of index have been considered. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1903.07096v2-abstract-full').style.display = 'none'; document.getElementById('1903.07096v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 December, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 17 March, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">in Russian (English abstract)</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1903.00189">arXiv:1903.00189</a> <span> [<a href="https://arxiv.org/pdf/1903.00189">pdf</a>, <a href="https://arxiv.org/ps/1903.00189">ps</a>, <a href="https://arxiv.org/format/1903.00189">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> On properties of Bernstein functions of several complex variables </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1903.00189v3-abstract-short" style="display: inline;"> A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables is given. Examples are considered. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1903.00189v3-abstract-full" style="display: none;"> A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables is given. Examples are considered. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1903.00189v3-abstract-full').style.display = 'none'; document.getElementById('1903.00189v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 March, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 1 March, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">in Russian</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47A60 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1903.00055">arXiv:1903.00055</a> <span> [<a href="https://arxiv.org/pdf/1903.00055">pdf</a>, <a href="https://arxiv.org/ps/1903.00055">ps</a>, <a href="https://arxiv.org/format/1903.00055">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Interpolation sets of algebras of generalized analytic functions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a>, <a href="/search/math?searchtype=author&query=Romanova%2C+M+A">M. A. Romanova</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1903.00055v1-abstract-short" style="display: inline;"> The properties of the compactness of interpolation sets of algebras of generalized analytic functions are investigated and convenient sufficient conditions for interpolation are given. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1903.00055v1-abstract-full" style="display: none;"> The properties of the compactness of interpolation sets of algebras of generalized analytic functions are investigated and convenient sufficient conditions for interpolation are given. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1903.00055v1-abstract-full').style.display = 'none'; document.getElementById('1903.00055v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 28 February, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">in Russian</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 43A </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1903.00051">arXiv:1903.00051</a> <span> [<a href="https://arxiv.org/pdf/1903.00051">pdf</a>, <a href="https://arxiv.org/ps/1903.00051">ps</a>, <a href="https://arxiv.org/format/1903.00051">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> On Shilov boundary and Gelfand spectrum of algebras of generalized analytic functions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1903.00051v2-abstract-short" style="display: inline;"> Let $S$ be a discrete abelian semigroup with unit and concellations and $\widehat {S}$ the semigroup of semicharacters of $S$. We shaw that the strong boundary and the Shilov boundary of the algebra of generalized analytic functions defined on $\widehat {S}$ are unions of some maximal subgroups of $\widehat {S}$. We shaw also that the both boundaries coincide with the character group of $S$ if… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1903.00051v2-abstract-full').style.display = 'inline'; document.getElementById('1903.00051v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1903.00051v2-abstract-full" style="display: none;"> Let $S$ be a discrete abelian semigroup with unit and concellations and $\widehat {S}$ the semigroup of semicharacters of $S$. We shaw that the strong boundary and the Shilov boundary of the algebra of generalized analytic functions defined on $\widehat {S}$ are unions of some maximal subgroups of $\widehat {S}$. We shaw also that the both boundaries coincide with the character group of $S$ if $S$ does not contain nontrivial simple ideals. In the last case the Gelfand spectrum of the algebra under consideration is calculated. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1903.00051v2-abstract-full').style.display = 'none'; document.getElementById('1903.00051v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 March, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 28 February, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">in Russian</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 43A; </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1902.11234">arXiv:1902.11234</a> <span> [<a href="https://arxiv.org/pdf/1902.11234">pdf</a>, <a href="https://arxiv.org/ps/1902.11234">ps</a>, <a href="https://arxiv.org/format/1902.11234">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Some assertions that are equivalent to Riemann hypothesis </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1902.11234v1-abstract-short" style="display: inline;"> Some assertions in harmonic analysis on the infinite dimensional torus are stated and their equivalence to Riemann hypothesis is proved. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1902.11234v1-abstract-full" style="display: none;"> Some assertions in harmonic analysis on the infinite dimensional torus are stated and their equivalence to Riemann hypothesis is proved. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1902.11234v1-abstract-full').style.display = 'none'; document.getElementById('1902.11234v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 28 February, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">in Russian</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 11M </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1902.11215">arXiv:1902.11215</a> <span> [<a href="https://arxiv.org/pdf/1902.11215">pdf</a>, <a href="https://arxiv.org/ps/1902.11215">ps</a>, <a href="https://arxiv.org/format/1902.11215">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> The Paley-Wiener-Gelfand tauberian theorem for semigroups with invariant measure </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1902.11215v2-abstract-short" style="display: inline;"> The theorem is proved that generalizes the Gelfand generalization of the Paley-Wiener tauberian theorem to general abelian topological semigroups with invariant measure. Several corollaries of this theorem are given. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1902.11215v2-abstract-full" style="display: none;"> The theorem is proved that generalizes the Gelfand generalization of the Paley-Wiener tauberian theorem to general abelian topological semigroups with invariant measure. Several corollaries of this theorem are given. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1902.11215v2-abstract-full').style.display = 'none'; document.getElementById('1902.11215v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 September, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 28 February, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">in Russian</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 40E05; 43A70 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1902.08762">arXiv:1902.08762</a> <span> [<a href="https://arxiv.org/pdf/1902.08762">pdf</a>, <a href="https://arxiv.org/ps/1902.08762">ps</a>, <a href="https://arxiv.org/format/1902.08762">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> On multidimensional Bochner-Phillips functional calculus </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1902.08762v1-abstract-short" style="display: inline;"> The functional calculus of semigroup generators, based on the class of Bernstein functions in several variables is developed, the condition for holomorphy of semigroups, generated by operators which arisen in the calculus is given, and in the one-dimensional case the moment inequality for such operators is proved. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1902.08762v1-abstract-full" style="display: none;"> The functional calculus of semigroup generators, based on the class of Bernstein functions in several variables is developed, the condition for holomorphy of semigroups, generated by operators which arisen in the calculus is given, and in the one-dimensional case the moment inequality for such operators is proved. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1902.08762v1-abstract-full').style.display = 'none'; document.getElementById('1902.08762v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 February, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">in Russian</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47A60 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1902.08655">arXiv:1902.08655</a> <span> [<a href="https://arxiv.org/pdf/1902.08655">pdf</a>, <a href="https://arxiv.org/ps/1902.08655">ps</a>, <a href="https://arxiv.org/format/1902.08655">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> On the essential spectrum of $位$-Toeplitz operators over compact Abelian groups </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1902.08655v1-abstract-short" style="display: inline;"> In the recent paper by Mark C. Ho (2014) the notion of a $位$-Toeplitz operator on the Hardy space $H^2(\mathbb{T})$ over the one-dimensional torus $\mathbb{T}$ was introduced and it was shown (under the supplementary condition) that for $位\in \mathbb{T}$ the essential spectrum of such an operator is invariant with respect to the rotation $z\mapsto 位z$; if in addition $位$ is not of finite order the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1902.08655v1-abstract-full').style.display = 'inline'; document.getElementById('1902.08655v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1902.08655v1-abstract-full" style="display: none;"> In the recent paper by Mark C. Ho (2014) the notion of a $位$-Toeplitz operator on the Hardy space $H^2(\mathbb{T})$ over the one-dimensional torus $\mathbb{T}$ was introduced and it was shown (under the supplementary condition) that for $位\in \mathbb{T}$ the essential spectrum of such an operator is invariant with respect to the rotation $z\mapsto 位z$; if in addition $位$ is not of finite order the essential spectrum is circular. In this paper, we generalize these results to the case when $\mathbb{T}$ is replaced by an arbitrary compact Abelian group whose dual is totally ordered. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1902.08655v1-abstract-full').style.display = 'none'; document.getElementById('1902.08655v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 February, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47B35; 47A17 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. Math. Anal. Appl., 424, no. 2, 1286 - 1295 (2015) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1902.08650">arXiv:1902.08650</a> <span> [<a href="https://arxiv.org/pdf/1902.08650">pdf</a>, <a href="https://arxiv.org/ps/1902.08650">ps</a>, <a href="https://arxiv.org/format/1902.08650">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Functions of bounded mean oscillation and Hankel operators on compact abelian groups </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a>, <a href="/search/math?searchtype=author&query=Dyba%2C+R+V">R. V. Dyba</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1902.08650v1-abstract-short" style="display: inline;"> Generalization of functions of bounded mean oscillation and Hankel operators to the case of compact abelian groups with linearly ordered dual is considered. Spaces of functions of bounded mean oscillation and of bounded mean oscillation of analytic type on such groups are described in terms of boundedness of corresponding Hankel operators under the assumption that the dual group contains a minimal… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1902.08650v1-abstract-full').style.display = 'inline'; document.getElementById('1902.08650v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1902.08650v1-abstract-full" style="display: none;"> Generalization of functions of bounded mean oscillation and Hankel operators to the case of compact abelian groups with linearly ordered dual is considered. Spaces of functions of bounded mean oscillation and of bounded mean oscillation of analytic type on such groups are described in terms of boundedness of corresponding Hankel operators under the assumption that the dual group contains a minimal positive element. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1902.08650v1-abstract-full').style.display = 'none'; document.getElementById('1902.08650v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 February, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">in Russian</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47B35 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1902.08637">arXiv:1902.08637</a> <span> [<a href="https://arxiv.org/pdf/1902.08637">pdf</a>, <a href="https://arxiv.org/ps/1902.08637">ps</a>, <a href="https://arxiv.org/format/1902.08637">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> On some properties of multidimensional Bochner-Phillips functional calculus </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1902.08637v1-abstract-short" style="display: inline;"> The multidimensional functional calculus of semigroup generators, based on the class of Bernstein functions in several variables is developed, the spectral mapping theorems for joint spectra have been stated, the condition for holomorphy of semigroups, generated by operators which arises in the calculus is given, and the moment inequality for such operators is proved. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1902.08637v1-abstract-full" style="display: none;"> The multidimensional functional calculus of semigroup generators, based on the class of Bernstein functions in several variables is developed, the spectral mapping theorems for joint spectra have been stated, the condition for holomorphy of semigroups, generated by operators which arises in the calculus is given, and the moment inequality for such operators is proved. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1902.08637v1-abstract-full').style.display = 'none'; document.getElementById('1902.08637v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 February, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">in Russian</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47A60 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1902.08583">arXiv:1902.08583</a> <span> [<a href="https://arxiv.org/pdf/1902.08583">pdf</a>, <a href="https://arxiv.org/ps/1902.08583">ps</a>, <a href="https://arxiv.org/format/1902.08583">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Criteria for analyticity of subordinate semigroups </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1902.08583v2-abstract-short" style="display: inline;"> Let $蠄$ be a Bernstein function. A.~Carasso and T.~Kato obtained necessary and sufficient conditions for $蠄$ to have a property that $蠄(A)$ generates a quasibounded holomorphic semigroup for every generator $A$ of a bounded $C_0$-semigroup in a Banach space, in terms of some convolution semigroup of measures associated with $蠄$. We give an alternative to Carasso-Kato's criterium, and derive severa… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1902.08583v2-abstract-full').style.display = 'inline'; document.getElementById('1902.08583v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1902.08583v2-abstract-full" style="display: none;"> Let $蠄$ be a Bernstein function. A.~Carasso and T.~Kato obtained necessary and sufficient conditions for $蠄$ to have a property that $蠄(A)$ generates a quasibounded holomorphic semigroup for every generator $A$ of a bounded $C_0$-semigroup in a Banach space, in terms of some convolution semigroup of measures associated with $蠄$. We give an alternative to Carasso-Kato's criterium, and derive several sufficient conditions for $蠄$ to have the above-mentioned property. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1902.08583v2-abstract-full').style.display = 'none'; document.getElementById('1902.08583v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 September, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 February, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47A60; 47D03 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1902.08398">arXiv:1902.08398</a> <span> [<a href="https://arxiv.org/pdf/1902.08398">pdf</a>, <a href="https://arxiv.org/ps/1902.08398">ps</a>, <a href="https://arxiv.org/format/1902.08398">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> On joint spectra of families of unbounded operators </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1902.08398v1-abstract-short" style="display: inline;"> In this paper several joint spectra for a finite commuting family of closed operators in Banach space are considered, some new relations between these spectra established (earlier only the inclusion of the Taylor spectrum in the commutant one was known), and in the case of semigroup generators spectral mapping theorems for such spectra are proved. Several of this theorems are generalizations of pr… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1902.08398v1-abstract-full').style.display = 'inline'; document.getElementById('1902.08398v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1902.08398v1-abstract-full" style="display: none;"> In this paper several joint spectra for a finite commuting family of closed operators in Banach space are considered, some new relations between these spectra established (earlier only the inclusion of the Taylor spectrum in the commutant one was known), and in the case of semigroup generators spectral mapping theorems for such spectra are proved. Several of this theorems are generalizations of preceding results due to the author. Applications to stability of multiparametric semigroups are given. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1902.08398v1-abstract-full').style.display = 'none'; document.getElementById('1902.08398v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 February, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">in Russian</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47A10; 47A60; 47D03 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Izvestiya: Mathematics 79:6 1235 - 1259 (2015) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1902.07671">arXiv:1902.07671</a> <span> [<a href="https://arxiv.org/pdf/1902.07671">pdf</a>, <a href="https://arxiv.org/ps/1902.07671">ps</a>, <a href="https://arxiv.org/format/1902.07671">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> On the description of multidimensional normal Hausdorff operators on Lebesgue spaces </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1902.07671v2-abstract-short" style="display: inline;"> The main goal of this work is to examine the structure of normal Hausdorff operators on $\mathbb{R}^n$. We show that normal Hausdorff operator in $L^2(\mathbb{R}^n)$ is unitary equivalent to the operator of multiplication by some matrix-function (its matrix symbol) in the space $L^2(\mathbb{R}^n; \mathbb{C}^{2^n}).$ Several corollaries that show that properties of a Hausdorff operator are closel… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1902.07671v2-abstract-full').style.display = 'inline'; document.getElementById('1902.07671v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1902.07671v2-abstract-full" style="display: none;"> The main goal of this work is to examine the structure of normal Hausdorff operators on $\mathbb{R}^n$. We show that normal Hausdorff operator in $L^2(\mathbb{R}^n)$ is unitary equivalent to the operator of multiplication by some matrix-function (its matrix symbol) in the space $L^2(\mathbb{R}^n; \mathbb{C}^{2^n}).$ Several corollaries that show that properties of a Hausdorff operator are closely related to the properties of its symbol are considered. In particular, the norm and the spectrum of such operators are described in terms of the symbol. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1902.07671v2-abstract-full').style.display = 'none'; document.getElementById('1902.07671v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 11 April, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 20 February, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47B38; 47B15; 46E30 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1812.02680">arXiv:1812.02680</a> <span> [<a href="https://arxiv.org/pdf/1812.02680">pdf</a>, <a href="https://arxiv.org/ps/1812.02680">ps</a>, <a href="https://arxiv.org/format/1812.02680">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> The structure of normal Hausdorff operators on Lebesgue spaces </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1812.02680v2-abstract-short" style="display: inline;"> We consider a generalization of Hausdorff operator and introduce the notion of the symbol of such an operator. Using this notion we describe the structure and investigate important properties (such as invertibility, spectrum, norm, and compactness) of normal generalized Hausdorff operators on Lebesgue spaces over $\mathbb{R}^n.$ The examples of Ces脿ro operators are considered. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1812.02680v2-abstract-full" style="display: none;"> We consider a generalization of Hausdorff operator and introduce the notion of the symbol of such an operator. Using this notion we describe the structure and investigate important properties (such as invertibility, spectrum, norm, and compactness) of normal generalized Hausdorff operators on Lebesgue spaces over $\mathbb{R}^n.$ The examples of Ces脿ro operators are considered. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1812.02680v2-abstract-full').style.display = 'none'; document.getElementById('1812.02680v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 December, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 6 December, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47B38; 47B15; 46E30 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1808.08257">arXiv:1808.08257</a> <span> [<a href="https://arxiv.org/pdf/1808.08257">pdf</a>, <a href="https://arxiv.org/ps/1808.08257">ps</a>, <a href="https://arxiv.org/format/1808.08257">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Boundedness of Hausdorff operators on Hardy spaces $H^1$ over locally compact groups </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A">Adolf Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1808.08257v5-abstract-short" style="display: inline;"> Results of Liflyand and collaborators on the boundedness of Hausdorff operators on the Hardy space $H^1$ over finite-dimensional real space generalized to the case of locally compact groups that are spaces of homogeneous type. Special cases and examples of compact Lie groups, homogeneous groups (in particular the Heisenberg group) and finite-dimensional spaces over division rings are considered. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1808.08257v5-abstract-full" style="display: none;"> Results of Liflyand and collaborators on the boundedness of Hausdorff operators on the Hardy space $H^1$ over finite-dimensional real space generalized to the case of locally compact groups that are spaces of homogeneous type. Special cases and examples of compact Lie groups, homogeneous groups (in particular the Heisenberg group) and finite-dimensional spaces over division rings are considered. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1808.08257v5-abstract-full').style.display = 'none'; document.getElementById('1808.08257v5-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 November, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 24 August, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">The erratum is added to the previous version of the preprint</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47B38; 46E30; 22E30 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1806.05066">arXiv:1806.05066</a> <span> [<a href="https://arxiv.org/pdf/1806.05066">pdf</a>, <a href="https://arxiv.org/ps/1806.05066">ps</a>, <a href="https://arxiv.org/format/1806.05066">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Perturbation determinants on Banach spaces and operator differentiability for Hirsch functional calculus </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A">Adolf Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1806.05066v4-abstract-short" style="display: inline;"> We consider a perturbation determinant for pairs of nonpositive (in a sense of Komatsu) operators on Banach space with nuclear difference and prove a generalization of the important formula for the logarithmic derivative of this determinant. To this end the Frechet differentiability of operator monotonic (negative complete Bernstein) functions of negative and nonpositive operators on Banach spaces… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1806.05066v4-abstract-full').style.display = 'inline'; document.getElementById('1806.05066v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1806.05066v4-abstract-full" style="display: none;"> We consider a perturbation determinant for pairs of nonpositive (in a sense of Komatsu) operators on Banach space with nuclear difference and prove a generalization of the important formula for the logarithmic derivative of this determinant. To this end the Frechet differentiability of operator monotonic (negative complete Bernstein) functions of negative and nonpositive operators on Banach spaces is investigated. The results may be regarded as a contribution to the Hirsch functional calculus. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1806.05066v4-abstract-full').style.display = 'none'; document.getElementById('1806.05066v4-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 September, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 12 June, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">arXiv admin note: text overlap with arXiv:1805.01337</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47A56; 47B10; 47L20 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1805.01337">arXiv:1805.01337</a> <span> [<a href="https://arxiv.org/pdf/1805.01337">pdf</a>, <a href="https://arxiv.org/ps/1805.01337">ps</a>, <a href="https://arxiv.org/format/1805.01337">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Lifshitz-Krein trace formula for Hirsch functiuonal calculus on Banach spaces </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">Adolf R Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1805.01337v6-abstract-short" style="display: inline;"> We give a simple definition of a spectral shift function for pairs of nonpositive operators on Banach spaces and prove trace formulas of Lifshitz-Kre沫n type for a perturbation of an operator monotonic (negative complete Bernstein) function of negative and nonpositive operators on Banach spaces induced by nuclear perturbation of an operator argument. The Lipschitzness of such functions is also inve… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1805.01337v6-abstract-full').style.display = 'inline'; document.getElementById('1805.01337v6-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1805.01337v6-abstract-full" style="display: none;"> We give a simple definition of a spectral shift function for pairs of nonpositive operators on Banach spaces and prove trace formulas of Lifshitz-Kre沫n type for a perturbation of an operator monotonic (negative complete Bernstein) function of negative and nonpositive operators on Banach spaces induced by nuclear perturbation of an operator argument. The Lipschitzness of such functions is also investigated. The results may be regarded as a contribution to a perturbation theory for Hirsch functional calculus. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1805.01337v6-abstract-full').style.display = 'none'; document.getElementById('1805.01337v6-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 September, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 3 May, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> Primary 47A56; Secondary 47A55; 47B10; 47L20 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1802.01003">arXiv:1802.01003</a> <span> [<a href="https://arxiv.org/pdf/1802.01003">pdf</a>, <a href="https://arxiv.org/ps/1802.01003">ps</a>, <a href="https://arxiv.org/format/1802.01003">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Bernstein functions of several semigroup generators on Banach spaces under bounded perturbations. II </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1802.01003v1-abstract-short" style="display: inline;"> The paper deals with multidimensional Bochner-Phillips functional calculus. In the previous paper by the author bounded perturbations of Bernstein functions of several commuting semigroup generators on Banach spaces where considered, conditions for Lipschitzness and estimates for the norm of commutators of such functions where proved. Also in the one-dimensional case the Frechet differentiability… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1802.01003v1-abstract-full').style.display = 'inline'; document.getElementById('1802.01003v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1802.01003v1-abstract-full" style="display: none;"> The paper deals with multidimensional Bochner-Phillips functional calculus. In the previous paper by the author bounded perturbations of Bernstein functions of several commuting semigroup generators on Banach spaces where considered, conditions for Lipschitzness and estimates for the norm of commutators of such functions where proved. Also in the one-dimensional case the Frechet differentiability of Bernstein functions of semigroup generators on Banach spaces where proved and a generalization of Livschits-Kre沫n trace formula derived. The aim of the present paper is to prove the Frechet differentiability of operator Bernstein functions and the Livschits-Kre沫n trace formula in the multidimensional setting. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1802.01003v1-abstract-full').style.display = 'none'; document.getElementById('1802.01003v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 3 February, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">arXiv admin note: text overlap with arXiv:1611.06558</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 47A56; 47B10; 47L20 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1707.01291">arXiv:1707.01291</a> <span> [<a href="https://arxiv.org/pdf/1707.01291">pdf</a>, <a href="https://arxiv.org/ps/1707.01291">ps</a>, <a href="https://arxiv.org/format/1707.01291">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> On contractibility of the Gelfand spectrum of semigroup measure algebras </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1707.01291v2-abstract-short" style="display: inline;"> Sufficient conditions for a semigroup measure algebra to have contractible Gelfand spectrum are given and it is shown that for a wide class of semigroups these conditions are also necessary. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1707.01291v2-abstract-full" style="display: none;"> Sufficient conditions for a semigroup measure algebra to have contractible Gelfand spectrum are given and it is shown that for a wide class of semigroups these conditions are also necessary. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1707.01291v2-abstract-full').style.display = 'none'; document.getElementById('1707.01291v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 March, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 5 July, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">4 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 28A60 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1611.06584">arXiv:1611.06584</a> <span> [<a href="https://arxiv.org/pdf/1611.06584">pdf</a>, <a href="https://arxiv.org/ps/1611.06584">ps</a>, <a href="https://arxiv.org/format/1611.06584">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> The Markov-Stieltjes transform as an operator </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a>, <a href="/search/math?searchtype=author&query=Kovalyova%2C+I+S">I. S. Kovalyova</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1611.06584v1-abstract-short" style="display: inline;"> We prove that the Markov-Stieltjes transform is a bounded non compact Hankel operator on Hardy space $H^p$ with Hilbert matrix with respect to the standard Schauder basis of $H^p$ and a bounded non compact operator on Lebesgue space $L^p[0,1]$ for $p\in(1,\infty)$ and obtain estimates for its norm in this spaces. It is shown that the Markov-Stieltjes transform on $L^2(0,1)$ is unitary equivalent t… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1611.06584v1-abstract-full').style.display = 'inline'; document.getElementById('1611.06584v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1611.06584v1-abstract-full" style="display: none;"> We prove that the Markov-Stieltjes transform is a bounded non compact Hankel operator on Hardy space $H^p$ with Hilbert matrix with respect to the standard Schauder basis of $H^p$ and a bounded non compact operator on Lebesgue space $L^p[0,1]$ for $p\in(1,\infty)$ and obtain estimates for its norm in this spaces. It is shown that the Markov-Stieltjes transform on $L^2(0,1)$ is unitary equivalent to the Markov-Stieltjes transform on $H^2$. Inverse formulas and operational properties for this transform are obtained. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1611.06584v1-abstract-full').style.display = 'none'; document.getElementById('1611.06584v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 November, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2016. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1611.06564">arXiv:1611.06564</a> <span> [<a href="https://arxiv.org/pdf/1611.06564">pdf</a>, <a href="https://arxiv.org/ps/1611.06564">ps</a>, <a href="https://arxiv.org/format/1611.06564">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Hankel Operators over Compact Abelian Groups </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a>, <a href="/search/math?searchtype=author&query=Kuzmenkova%2C+E+Y">E. Yu. Kuzmenkova</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1611.06564v1-abstract-short" style="display: inline;"> Two variants of generalizations of Hankel operators to the case of linearly ordered abelian groups are considered, criteria of the boundedness and compactness of these operators are given, among them in terms of functions of bounded mean oscillation, the nonfredholmness of generalized Hankel operators is proved. Some applications to the theory of Toeplitz operators on groups are given. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1611.06564v1-abstract-full" style="display: none;"> Two variants of generalizations of Hankel operators to the case of linearly ordered abelian groups are considered, criteria of the boundedness and compactness of these operators are given, among them in terms of functions of bounded mean oscillation, the nonfredholmness of generalized Hankel operators is proved. Some applications to the theory of Toeplitz operators on groups are given. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1611.06564v1-abstract-full').style.display = 'none'; document.getElementById('1611.06564v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 November, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">in Russian</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1611.06560">arXiv:1611.06560</a> <span> [<a href="https://arxiv.org/pdf/1611.06560">pdf</a>, <a href="https://arxiv.org/ps/1611.06560">ps</a>, <a href="https://arxiv.org/format/1611.06560">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Some topics in the perturbation theory for a functional calculus of closed operators on Banach spaces </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1611.06560v1-abstract-short" style="display: inline;"> The wark is a contribution to the functional calculus constructed by of the author and A. A. Atvinovskii of closed operators on Banach spaces. The calculus is based on Markov and related functions as symbols. Estimates of bounded perturbations of operator functions with respect to general operator ideal norms, operator Lipschitzness, moment inequality, Freshet operator differentiability, and Livsh… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1611.06560v1-abstract-full').style.display = 'inline'; document.getElementById('1611.06560v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1611.06560v1-abstract-full" style="display: none;"> The wark is a contribution to the functional calculus constructed by of the author and A. A. Atvinovskii of closed operators on Banach spaces. The calculus is based on Markov and related functions as symbols. Estimates of bounded perturbations of operator functions with respect to general operator ideal norms, operator Lipschitzness, moment inequality, Freshet operator differentiability, and Livshitz-Krein trace formulae have been considered. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1611.06560v1-abstract-full').style.display = 'none'; document.getElementById('1611.06560v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 November, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">in Russian</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1611.06559">arXiv:1611.06559</a> <span> [<a href="https://arxiv.org/pdf/1611.06559">pdf</a>, <a href="https://arxiv.org/ps/1611.06559">ps</a>, <a href="https://arxiv.org/format/1611.06559">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> A sufficient condition for global operator monotonicity for functions in several variables </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1611.06559v1-abstract-short" style="display: inline;"> The note contains two remarks to the authors note (Mathematical Notes, Vol. 94, 2013, p. 154 -- 156; in Russian) which was also devoted to sufficient conditions of global operator monotonicity. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1611.06559v1-abstract-full" style="display: none;"> The note contains two remarks to the authors note (Mathematical Notes, Vol. 94, 2013, p. 154 -- 156; in Russian) which was also devoted to sufficient conditions of global operator monotonicity. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1611.06559v1-abstract-full').style.display = 'none'; document.getElementById('1611.06559v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 November, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">in Russian</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1611.06558">arXiv:1611.06558</a> <span> [<a href="https://arxiv.org/pdf/1611.06558">pdf</a>, <a href="https://arxiv.org/ps/1611.06558">ps</a>, <a href="https://arxiv.org/format/1611.06558">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> Bounded perturbations of Bernstein functions of several operator variables </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1611.06558v1-abstract-short" style="display: inline;"> The paper deals with (multidimensional and one-dimensional) Bochner-Phillips functional calculus. Bounded perturbations of Bernstein functions of (one or several commuting) semigroup generators on Banach spaces are considered, conditions for Lipschitzness and Frechet-differentiability of such functions are obtained, estimates for the norm of commutators are proved, and a generalization of Livschit… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1611.06558v1-abstract-full').style.display = 'inline'; document.getElementById('1611.06558v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1611.06558v1-abstract-full" style="display: none;"> The paper deals with (multidimensional and one-dimensional) Bochner-Phillips functional calculus. Bounded perturbations of Bernstein functions of (one or several commuting) semigroup generators on Banach spaces are considered, conditions for Lipschitzness and Frechet-differentiability of such functions are obtained, estimates for the norm of commutators are proved, and a generalization of Livschits-Kre沫n trace formula derived. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1611.06558v1-abstract-full').style.display = 'none'; document.getElementById('1611.06558v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 November, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2016. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1610.04762">arXiv:1610.04762</a> <span> [<a href="https://arxiv.org/pdf/1610.04762">pdf</a>, <a href="https://arxiv.org/ps/1610.04762">ps</a>, <a href="https://arxiv.org/format/1610.04762">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Functional Analysis">math.FA</span> </div> </div> <p class="title is-5 mathjax"> On the general form of linear functionals on the Hardy spaces $H^1$ over compact Abelian groups and some of its applications </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Mirotin%2C+A+R">A. R. Mirotin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1610.04762v2-abstract-short" style="display: inline;"> The celebrated Fefferman's theorems on the general form of linear functionals on the Hardy space $H^1$ over the circle group is generalized to the case of an arbitrary compact Abelian group with totally ordered dual. Several corollaries that can be applied to multiple lacunary Fourier series and atomic decomposition on the two dimensional torus are obtained. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1610.04762v2-abstract-full" style="display: none;"> The celebrated Fefferman's theorems on the general form of linear functionals on the Hardy space $H^1$ over the circle group is generalized to the case of an arbitrary compact Abelian group with totally ordered dual. Several corollaries that can be applied to multiple lacunary Fourier series and atomic decomposition on the two dimensional torus are obtained. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1610.04762v2-abstract-full').style.display = 'none'; document.getElementById('1610.04762v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 November, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 15 October, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">14 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 43A17 43A70 </p> </li> </ol> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary">  <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul class="nav-spaced"> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 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