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Functional Analysis
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id="recent-math.FA" aria-labelledby="recent-math.FA" href="/list/math.FA/recent">recent</a> articles</p> <h3>Showing new listings for Tuesday, 26 November 2024</h3> <div class='paging'>Total of 17 entries </div> <div class='morefewer'>Showing up to 2000 entries per page: <a href=/list/math.FA/new?skip=0&show=1000 rel="nofollow"> fewer</a> | <span style="color: #454545">more</span> | <span style="color: #454545">all</span> </div> <dl id='articles'> <h3>New submissions (showing 7 of 7 entries)</h3> <dt> <a name='item1'>[1]</a> <a href ="/abs/2411.15141" title="Abstract" id="2411.15141"> arXiv:2411.15141 </a> [<a href="/pdf/2411.15141" title="Download PDF" id="pdf-2411.15141" aria-labelledby="pdf-2411.15141">pdf</a>, <a href="https://arxiv.org/html/2411.15141v1" title="View HTML" id="html-2411.15141" aria-labelledby="html-2411.15141" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.15141" title="Other formats" id="oth-2411.15141" aria-labelledby="oth-2411.15141">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Comparability of Metrics and Norms in terms of Basis of Exponential Vector Space </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Biswas,+D+P">Dhruba Prakash Biswas</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Sharma,+P">Priti Sharma</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Jana,+S">Sandip Jana</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Schwaiger,+J">Jens Schwaiger</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> arXiv admin note: text overlap with <a href="https://arxiv.org/abs/2305.12154" data-arxiv-id="2305.12154" class="link-https">arXiv:2305.12154</a> </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Functional Analysis (math.FA)</span> </div> <p class='mathjax'> In this paper, we shall compare two metrics in terms of orderly dependence, a notion developed in exponential vector space in the article 'Basis and Dimension of Exponential Vector Space' by Jayeeta Saha and Sandip Jana in Transactions of A. Razmadze Mathematical Institute Vol. 175 (2021), issue 1, 101-115. Exponential vector space, in short 'evs', is a partially ordered space associated with a commutative semigroup structure and a compatible scalar multiplication. In the present paper we shall show that the collection $\mathcal{D(\mathbf X)}$ of all metrics on a non-empty set $\mathbf X$, together with the constant function zero $O$, forms a topological exponential vector space. We shall discuss the orderly dependence of two metrics through our findings of a basis of $\mathcal{D(\mathbf X)}\smallsetminus\{O\}$ in different scenario. We shall characterise orderly independence of two elements of a topological evs in terms of the comparing function, another mechanism developed in topological exponential vector space, which can measure the degree of comparability of two elements of an evs. Finally, we shall discuss existence of orderly independent norms on a linear space. For an infinite dimensional linear space we shall construct a large number of orderly independent norms depending on the dimension of the linear space. Orderly independent norms are precisely those which are totally non-equivalent, in the sense that they produce incomparable topologies. </p> </div> </dd> <dt> <a name='item2'>[2]</a> <a href ="/abs/2411.15379" title="Abstract" id="2411.15379"> arXiv:2411.15379 </a> [<a href="/pdf/2411.15379" title="Download PDF" id="pdf-2411.15379" aria-labelledby="pdf-2411.15379">pdf</a>, <a href="https://arxiv.org/html/2411.15379v1" title="View HTML" id="html-2411.15379" aria-labelledby="html-2411.15379" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.15379" title="Other formats" id="oth-2411.15379" aria-labelledby="oth-2411.15379">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Mixed-Fourier-norm spaces and holomorphic functions </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Avetisyan,+Z">Zhirayr Avetisyan</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Karapetyants,+A">Alexey Karapetyants</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Functional Analysis (math.FA)</span> </div> <p class='mathjax'> We describe a general framework of functional and Fourier analysis on domains with a free action of an Abelian Lie group $G$. Namely, on a domain of the form $G\times Y$ we introduce the appropriate spaces of distributions and measurable functions, establishing their most basic properties. Then we consider the half-Fourier transform $f(x,y)\mapsto\hat f(\xi,y)$ in the first variable, and discuss the behaviour of function spaces on $G\times Y$ and $\hat G\times Y$ under this transform. We introduce general mixed-Fourier-norm spaces on $G\times Y$, and the subspaces of holomorphic functions among them, and give an explicit descriptions of the Fourier images of these spaces. </p> </div> </dd> <dt> <a name='item3'>[3]</a> <a href ="/abs/2411.15475" title="Abstract" id="2411.15475"> arXiv:2411.15475 </a> [<a href="/pdf/2411.15475" title="Download PDF" id="pdf-2411.15475" aria-labelledby="pdf-2411.15475">pdf</a>, <a href="https://arxiv.org/html/2411.15475v1" title="View HTML" id="html-2411.15475" aria-labelledby="html-2411.15475" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.15475" title="Other formats" id="oth-2411.15475" aria-labelledby="oth-2411.15475">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Advancements in nonlinear exponential sampling: convergence, quantitative analysis and Voronovskaya-type formula </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Costarelli,+D">Danilo Costarelli</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Natale,+M">Mariarosaria Natale</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Functional Analysis (math.FA)</span> </div> <p class='mathjax'> In this paper, we introduce the nonlinear exponential Kantorovich sampling series. We establish pointwise and uniform convergence properties and a nonlinear asymptotic formula of the Voronovskaja-type given in terms of the limsup. Furthermore, we extend these convergence results to Mellin-Orlicz spaces with respect to the logarithmic (Haar) measure. Quantitative results are also given, using the log-modulus of continuity and the log-modulus of smoothness, respectively, for log-uniformly continuous functions and for functions in Mellin-Orlicz spaces. Consequently, the qualitative order of convergence can be obtained in case of functions belonging to suitable Lipschitz (log-H枚lderian) classes. </p> </div> </dd> <dt> <a name='item4'>[4]</a> <a href ="/abs/2411.15578" title="Abstract" id="2411.15578"> arXiv:2411.15578 </a> [<a href="/pdf/2411.15578" title="Download PDF" id="pdf-2411.15578" aria-labelledby="pdf-2411.15578">pdf</a>, <a href="https://arxiv.org/html/2411.15578v1" title="View HTML" id="html-2411.15578" aria-labelledby="html-2411.15578" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.15578" title="Other formats" id="oth-2411.15578" aria-labelledby="oth-2411.15578">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Functions of continuous Ces\'aro operators </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Mirotin,+A">Adolf Mirotin</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Functional Analysis (math.FA)</span> </div> <p class='mathjax'> 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. </p> </div> </dd> <dt> <a name='item5'>[5]</a> <a href ="/abs/2411.15636" title="Abstract" id="2411.15636"> arXiv:2411.15636 </a> [<a href="/pdf/2411.15636" title="Download PDF" id="pdf-2411.15636" aria-labelledby="pdf-2411.15636">pdf</a>, <a href="https://arxiv.org/html/2411.15636v1" title="View HTML" id="html-2411.15636" aria-labelledby="html-2411.15636" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.15636" title="Other formats" id="oth-2411.15636" aria-labelledby="oth-2411.15636">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Convergence of Complementable Operators </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Naik,+S+M">Sachin Manjunath Naik</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Johnson,+P+S">P. Sam Johnson</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Functional Analysis (math.FA)</span> </div> <p class='mathjax'> Complementable operators extend classical matrix decompositions, such as the Schur complement, to the setting of infinite-dimensional Hilbert spaces, thereby broadening their applicability in various mathematical and physical contexts. This paper focuses on the convergence properties of complementable operators, investigating when the limit of sequence of complementable operators remains complementable. We also explore the convergence of sequences and series of powers of complementable operators, providing new insights into their convergence behavior. Additionally, we examine the conditions under which the set of complementable operators is the subset of set of boundary points of the set of non-complementable operators with respect to the strong operator topology. The paper further explores the topological structure of the subset of complementable operators, offering a characterization of its closed subsets. </p> </div> </dd> <dt> <a name='item6'>[6]</a> <a href ="/abs/2411.16010" title="Abstract" id="2411.16010"> arXiv:2411.16010 </a> [<a href="/pdf/2411.16010" title="Download PDF" id="pdf-2411.16010" aria-labelledby="pdf-2411.16010">pdf</a>, <a href="https://arxiv.org/html/2411.16010v1" title="View HTML" id="html-2411.16010" aria-labelledby="html-2411.16010" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.16010" title="Other formats" id="oth-2411.16010" aria-labelledby="oth-2411.16010">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Uniform stability of concentration inequalities and applications </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=G%C3%B3mez,+J">Jaime G贸mez</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Kalaj,+D">David Kalaj</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Melentijevi%C4%87,+P">Petar Melentijevi膰</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Ramos,+J+P+G">Jo茫o P. G. Ramos</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 43 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Functional Analysis (math.FA)</span>; Classical Analysis and ODEs (math.CA); Complex Variables (math.CV) </div> <p class='mathjax'> We prove a sharp quantitative version of recent Faber-Krahn inequalities for the continuous Wavelet transforms associated to a certain family of Cauchy wavelet windows . Our results are uniform on the parameters of the family of Cauchy wavelets, and asymptotically sharp in both directions. <br>As a corollary of our results, we are able to recover not only the original result for the short-time Fourier transform as a limiting procedure, but also a new concentration result for functions in Hardy spaces. This is a completely novel result about optimal concentration of Poisson extensions, and our proof automatically comes with a sharp stability version of that inequality. <br>Our techniques highlight the intertwining of geometric and complex-analytic arguments involved in the context of concentration inequalities. In particular, in the process of deriving uniform results, we obtain a refinement over the proof of a previous result by the first and fourth authors together with A. Guerra and P. Tilli, further improving the current understanding of the geometry of near extremals in all contexts under consideration. </p> </div> </dd> <dt> <a name='item7'>[7]</a> <a href ="/abs/2411.16426" title="Abstract" id="2411.16426"> arXiv:2411.16426 </a> [<a href="/pdf/2411.16426" title="Download PDF" id="pdf-2411.16426" aria-labelledby="pdf-2411.16426">pdf</a>, <a href="/format/2411.16426" title="Other formats" id="oth-2411.16426" aria-labelledby="oth-2411.16426">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Trace formulas for $\mathcal{S}^p$-perturbations and extension of Koplienko-Neidhardt trace formulas </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Chattopadhyay,+A">Arup Chattopadhyay</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Coine,+C">Cl茅ment Coine</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Giri,+S">Saikat Giri</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Pradhan,+C">Chandan Pradhan</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 44 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Functional Analysis (math.FA)</span> </div> <p class='mathjax'> In this paper, we extend the class of admissible functions for the trace formula of the second order in the self-adjoint, unitary, and contraction cases for a perturbation in the Hilbert-Schmidt class $\mathcal{S}^2(\mathcal{H})$ by assuming a certain factorization of the divided difference $f^{[2]}$. This class is the natural one to ensure that the second order Taylor remainder is a trace class operator. It encompasses all the classes of functions for which the trace formula was previously known. Secondly, for a Schatten $\mathcal{S}^p$-perturbation, $1<p<\infty$, we prove general modified trace formulas for every $n$-times differentiable functions with bounded $n$-th derivative in the self-adjoint and unitary cases and for every $f$ such that $f$ and its derivatives are in the disk algebra $\mathcal{A}(\mathbb{D})$ in the contraction case. </p> </div> </dd> </dl> <dl id='articles'> <h3>Cross submissions (showing 4 of 4 entries)</h3> <dt> <a name='item8'>[8]</a> <a href ="/abs/2411.15273" title="Abstract" id="2411.15273"> arXiv:2411.15273 </a> (cross-list from math.OA) [<a href="/pdf/2411.15273" title="Download PDF" id="pdf-2411.15273" aria-labelledby="pdf-2411.15273">pdf</a>, <a href="https://arxiv.org/html/2411.15273v1" title="View HTML" id="html-2411.15273" aria-labelledby="html-2411.15273" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.15273" title="Other formats" id="oth-2411.15273" aria-labelledby="oth-2411.15273">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Birkhoff-James classification of finite-dimensional $C^*$-algebras </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Kuzma,+B">Bojan Kuzma</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Singla,+S">Sushil Singla</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> Accepted for publication in Proc. Amer. Math. Soc </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Operator Algebras (math.OA)</span>; Functional Analysis (math.FA) </div> <p class='mathjax'> We classify real or complex finite-dimensional $C^*$-algebras and their underlying fields from the properties of Birkhoff-James orthogonality. Application to strong Birkhoff-James orthogonality preservers is also given. </p> </div> </dd> <dt> <a name='item9'>[9]</a> <a href ="/abs/2411.15947" title="Abstract" id="2411.15947"> arXiv:2411.15947 </a> (cross-list from math.AP) [<a href="/pdf/2411.15947" title="Download PDF" id="pdf-2411.15947" aria-labelledby="pdf-2411.15947">pdf</a>, <a href="/format/2411.15947" title="Other formats" id="oth-2411.15947" aria-labelledby="oth-2411.15947">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Existence of Positive Solution for a System of Quasilinear Schrodinger </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Baig,+A">Ayesha Baig</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Zhouxin,+L">Li Zhouxin</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 26 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Analysis of PDEs (math.AP)</span>; Functional Analysis (math.FA) </div> <p class='mathjax'> We investigate the existence of standing wave solutions for quasilinear Schrodinger systems. To address the challenges posed by non differentiability, we adopt the dual approach introduced by Colin and Jeanjean. The existence of solutions is established using Del Pino and Felmer's penalization technique, with refinements inspired by Alves' arguments. </p> </div> </dd> <dt> <a name='item10'>[10]</a> <a href ="/abs/2411.16013" title="Abstract" id="2411.16013"> arXiv:2411.16013 </a> (cross-list from math.AP) [<a href="/pdf/2411.16013" title="Download PDF" id="pdf-2411.16013" aria-labelledby="pdf-2411.16013">pdf</a>, <a href="https://arxiv.org/html/2411.16013v1" title="View HTML" id="html-2411.16013" aria-labelledby="html-2411.16013" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.16013" title="Other formats" id="oth-2411.16013" aria-labelledby="oth-2411.16013">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Stochastic Analysis and White Noise Calculus of Nonlinear Wave Equations with Application to Laser Propagation and Generation </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=S.,+S">Sivaguru S. Sritharan</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Mudaliar,+S">Saba Mudaliar</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Analysis of PDEs (math.AP)</span>; Mathematical Physics (math-ph); Functional Analysis (math.FA); Probability (math.PR); Quantum Algebra (math.QA) </div> <p class='mathjax'> In this paper we study a large class of nonlinear stochastic wave equations that arise in laser generation models and models for propagation in random media in a unified mathematical framework. Continuous and pulse-wave propagation models, free electron laser generation models, as well as laser-plasma interaction models have been cast in a convenient and unified abstract framework as semilinear evolution equations in a Hilbert space to enable stochastic analysis. We formulate Ito calculus and white noise calculus methods of treating stochastic terms and prove existence and uniqueness of mild solutions. </p> </div> </dd> <dt> <a name='item11'>[11]</a> <a href ="/abs/2411.16261" title="Abstract" id="2411.16261"> arXiv:2411.16261 </a> (cross-list from math.DG) [<a href="/pdf/2411.16261" title="Download PDF" id="pdf-2411.16261" aria-labelledby="pdf-2411.16261">pdf</a>, <a href="https://arxiv.org/html/2411.16261v1" title="View HTML" id="html-2411.16261" aria-labelledby="html-2411.16261" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.16261" title="Other formats" id="oth-2411.16261" aria-labelledby="oth-2411.16261">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Almost-Fuchsian representations in PU(2,1) </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Bronstein,+S">Samuel Bronstein</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Differential Geometry (math.DG)</span>; Functional Analysis (math.FA); Geometric Topology (math.GT) </div> <p class='mathjax'> In this paper, we study nonmaximal representations of surface groups in PU(2,1). We show the existence in genus large enough, of convex-cocompact representations of nonmaximal Toledo invariant admitting a unique equivariant minimal surface, which is holomorphic and of second fundamental form arbitrarily small. These examples can be obtained for any Toledo invariant of the form 2-2g+(2/3)d, provided g is large compared to d. When d is not divisible by 3, this yields examples of convex-cocompact representations in PU(2,1) which do not lift to SU(2,1). </p> </div> </dd> </dl> <dl id='articles'> <h3>Replacement submissions (showing 6 of 6 entries)</h3> <dt> <a name='item12'>[12]</a> <a href ="/abs/2408.02864" title="Abstract" id="2408.02864"> arXiv:2408.02864 </a> (replaced) [<a href="/pdf/2408.02864" title="Download PDF" id="pdf-2408.02864" aria-labelledby="pdf-2408.02864">pdf</a>, <a href="https://arxiv.org/html/2408.02864v2" title="View HTML" id="html-2408.02864" aria-labelledby="html-2408.02864" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2408.02864" title="Other formats" id="oth-2408.02864" aria-labelledby="oth-2408.02864">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Distributions in spaces with thick submanifolds </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Ding,+J">Jiajia Ding</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Vindas,+J">Jasson Vindas</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Yang,+Y">Yunyun Yang</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 21 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Functional Analysis (math.FA)</span>; Analysis of PDEs (math.AP); Differential Geometry (math.DG) </div> <p class='mathjax'> We present the construction of a theory of distributions (generalized functions) with a ``thick submanifold'', that is, a new theory of thick distributions on $\mathbb{R}^n$ whose domain contains a smooth submanifold on which the test functions may be singular. We define several operations, including ``thick partial derivatives'', and clarify their connection with their classical counterparts in Schwartz distribution theory. We also introduce and study a number of special thick distributions, including new thick delta functions, or more generally thick multilayer distributions along a submanifold. </p> </div> </dd> <dt> <a name='item13'>[13]</a> <a href ="/abs/2410.08682" title="Abstract" id="2410.08682"> arXiv:2410.08682 </a> (replaced) [<a href="/pdf/2410.08682" title="Download PDF" id="pdf-2410.08682" aria-labelledby="pdf-2410.08682">pdf</a>, <a href="https://arxiv.org/html/2410.08682v2" title="View HTML" id="html-2410.08682" aria-labelledby="html-2410.08682" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2410.08682" title="Other formats" id="oth-2410.08682" aria-labelledby="oth-2410.08682">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Stability of shifts, interpolation, and crystalline measures </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Ulanovskii,+A">Alexander Ulanovskii</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Zlotnikov,+I">Ilya Zlotnikov</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 23 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Functional Analysis (math.FA)</span>; Classical Analysis and ODEs (math.CA) </div> <p class='mathjax'> Let $V^p_\Gamma(\mathcal{G}),1\leq p\leq\infty,$ be the quasi shift-invariant space generated by $\Gamma$-shifts of a function $\mathcal{G}$, where $\Gamma\subset\mathbb{R}$ is a separated set. For several large families of generators $\mathcal{G}$, we present necessary and sufficient conditions on $\Gamma$ that imply that the $\Gamma$-shifts of $\mathcal{G}$ form an unconditional basis for $V^p_\Gamma(\mathcal{G})$. The connection between this property, interpolation, universal interpolation, and crystalline measures is discussed. </p> </div> </dd> <dt> <a name='item14'>[14]</a> <a href ="/abs/2411.01339" title="Abstract" id="2411.01339"> arXiv:2411.01339 </a> (replaced) [<a href="/pdf/2411.01339" title="Download PDF" id="pdf-2411.01339" aria-labelledby="pdf-2411.01339">pdf</a>, <a href="https://arxiv.org/html/2411.01339v2" title="View HTML" id="html-2411.01339" aria-labelledby="html-2411.01339" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.01339" title="Other formats" id="oth-2411.01339" aria-labelledby="oth-2411.01339">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Composition operators on Paley-Wiener spaces </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Hai,+P+V">Pham Viet Hai</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Noor,+W">Waleed Noor</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Severiano,+O+R">Osmar Reis Severiano</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Functional Analysis (math.FA)</span> </div> <p class='mathjax'> We completely characterize the bounded composition operators $C_\phi f=f\circ\phi$ on the Paley-Wiener spaces $B^2_{\sigma}$ for $\sigma>0$ that are self-adjoint, unitary, cohyponormal, normal, complex symmetric and hypercyclic. Moreover, we show that if $\phi(0)\notin \mathbb{R}$ or $\phi(0)\in \mathbb{R}$ with $0<|\phi(0)|\leq 1$ (for this case, $\sigma<\pi$) then $C_{\phi}$ is cyclic on $B^2_{\sigma}.$ </p> </div> </dd> <dt> <a name='item15'>[15]</a> <a href ="/abs/2411.05539" title="Abstract" id="2411.05539"> arXiv:2411.05539 </a> (replaced) [<a href="/pdf/2411.05539" title="Download PDF" id="pdf-2411.05539" aria-labelledby="pdf-2411.05539">pdf</a>, <a href="https://arxiv.org/html/2411.05539v2" title="View HTML" id="html-2411.05539" aria-labelledby="html-2411.05539" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2411.05539" title="Other formats" id="oth-2411.05539" aria-labelledby="oth-2411.05539">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Ditkin sets for some functional spaces and applications to grand Lebesgue spaces </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=G%C3%BCrkanl%C4%B1,+A+T">A. Turan G眉rkanl谋</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 5 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Functional Analysis (math.FA)</span> </div> <p class='mathjax'> Let $G$ be a locally compact Abelian group with dual group $\widehat G $ and Haar measures $d\mu$ and $\hat d\mu$ respectively. In this work we have proved that if $X$ is an essential Banach ideal in Beurling algebra $ L^1_{\omega}(G),$ then a closed subset $E\subset \widehat G$ is a Ditkin set for $X$ if and only if $E$ is a Ditkin set for $ L^1_{\omega}(G).$ Next, as an application we have investigated the Ditkin sets for grand Lebesgue space $L^{p),\theta}(G)$ and Ditkin sets for $[L^p(G)]_{L^{p),\theta }}$, where $[L^p(G)]_{L^{p),\theta }}$ is the closure of the set $C_c(G)$ in $L^{p),\theta}(G)$. </p> </div> </dd> <dt> <a name='item16'>[16]</a> <a href ="/abs/2209.07803" title="Abstract" id="2209.07803"> arXiv:2209.07803 </a> (replaced) [<a href="/pdf/2209.07803" title="Download PDF" id="pdf-2209.07803" aria-labelledby="pdf-2209.07803">pdf</a>, <a href="https://arxiv.org/html/2209.07803v4" title="View HTML" id="html-2209.07803" aria-labelledby="html-2209.07803" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2209.07803" title="Other formats" id="oth-2209.07803" aria-labelledby="oth-2209.07803">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Generalized gravitational fields and well-posedness of the Boussinesq systems on non-compact Riemannian Manifolds </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Xuan,+P+T">Pham Truong Xuan</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Ngoc,+T+T">Tran Thi Ngoc</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 28 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Analysis of PDEs (math.AP)</span>; Mathematical Physics (math-ph); Differential Geometry (math.DG); Dynamical Systems (math.DS); Functional Analysis (math.FA) </div> <p class='mathjax'> We study the global existence, uniqueness and exponential stability of mild solutions to the Boussinesq systems equipped with a generalized gravitational field on the framework of non-compact Riemannian manifolds. We work on some manifolds satisfying some bounded and negative conditions on curvature tensors. We consider a couple of Stokes and heat semigroups associated with the corresponding linear system which provides a vectorial matrix semigoup. By using dispersive and smoothing estimates of the vectorial matrix semigroup we establish the global-in-time existence and uniqueness of mild solutions for linear systems. Next, we can pass from the linear system to the semilinear systems to obtain the well-posedness by using fixed point arguments. Moreover, we will prove the exponential stability of such solutions by using Gronwall's inequality. </p> </div> </dd> <dt> <a name='item17'>[17]</a> <a href ="/abs/2407.04410" title="Abstract" id="2407.04410"> arXiv:2407.04410 </a> (replaced) [<a href="/pdf/2407.04410" title="Download PDF" id="pdf-2407.04410" aria-labelledby="pdf-2407.04410">pdf</a>, <a href="https://arxiv.org/html/2407.04410v5" title="View HTML" id="html-2407.04410" aria-labelledby="html-2407.04410" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2407.04410" title="Other formats" id="oth-2407.04410" aria-labelledby="oth-2407.04410">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> On the Existence of an Extremal Function for the Delsarte Extremal Problem </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Ramabulana,+M+D">Mita Dimpho Ramabulana</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Classical Analysis and ODEs (math.CA)</span>; Functional Analysis (math.FA) </div> <p class='mathjax'> In the general setting of a locally compact Abelian group $G$, the Delsarte extremal problem asks for the supremum of integrals over the collection of continuous positive definite functions $f: G \to \mathbb{R}$ satisfying $f(0) = 1$ and having $\mathrm{supp} f_{+} \subset \Omega$ for some measurable subset $\Omega$ of finite measure. In this paper, we consider the question of the existence of an extremal function for the Delsarte extremal problem. In particular, we show that there exists an extremal function for the Delsarte problem when $\Omega$ is closed, extending previously known existence results to a larger class of functions. </p> </div> </dd> </dl> <div class='paging'>Total of 17 entries </div> <div class='morefewer'>Showing up to 2000 entries per page: <a href=/list/math.FA/new?skip=0&show=1000 rel="nofollow"> fewer</a> | <span style="color: #454545">more</span> | <span style="color: #454545">all</span> </div> </div> </div> </div> </main> <footer style="clear: both;"> <div class="columns is-desktop" role="navigation" aria-label="Secondary" style="margin: -0.75em -0.75em 0.75em -0.75em"> <!-- Macro-Column 1 --> <div class="column" style="padding: 0;"> <div class="columns"> <div class="column"> <ul style="list-style: none; line-height: 2;"> <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 style="list-style: none; line-height: 2;"> <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 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg> <a href="https://info.arxiv.org/help/contact.html"> Contact</a> </li> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>subscribe to arXiv mailings</title><desc>Click here to subscribe</desc><path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z"/></svg> <a href="https://info.arxiv.org/help/subscribe"> Subscribe</a> </li> </ul> </div> </div> </div> <!-- End Macro-Column 1 --> <!-- Macro-Column 2 --> <div class="column" style="padding: 0;"> <div class="columns"> <div class="column"> <ul style="list-style: none; 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