Document Zbl 08012135

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Math.</a> <a href="/?q=in%3A525812" title="Articles in this Issue">280, No. 3, 247-268 (2025)</a>. </div> <div class="abstract">Summary: We construct two classes of Moran frame spectral measures on $\mathbb{R}^d$. Moreover, we prove that the Beurling dimensions of any frame spectrum of the two classes of Moran frame spectral measures are not greater than the Hausdorff dimensions of their supports, and under some mild conditions, the upper bounds can be attained.</div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A42C15" title="MSC2020">42C15</a> </td> <td class="space"> General harmonic expansions, frames </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A42B05" title="MSC2020">42B05</a> </td> <td class="space"> Fourier series and coefficients in several variables </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A42A85" title="MSC2020">42A85</a> </td> <td class="space"> Convolution, factorization for one variable harmonic analysis </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A28A80" title="MSC2020">28A80</a> </td> <td class="space"> Fractals </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A28A25" title="MSC2020">28A25</a> </td> <td class="space"> Integration with respect to measures and other set functions </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3ABeurling+dimension">Beurling dimension</a>; <a href="/?q=ut%3AFourier+frame">Fourier frame</a>; <a href="/?q=ut%3AHausdorff+dimension">Hausdorff dimension</a>; <a href="/?q=ut%3AMoran+measure">Moran measure</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 08012135" data-ciurl="/ci/08012135" data-biburl="/bibtex/08012135.bib" data-amsurl="/amsrefs/08012135.bib" data-xmlurl="/xml/08012135.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/08012135.pdf" title="Zbl 08012135 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.4064/sm240305-25-9" aria-label="DOI for “Moran frame spectral measure and Beurling dimension”" title="10.4064/sm240305-25-9">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">L. 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Math. 81 (2000), 209-238. · <a href="/0976.42020" class="nowrap">Zbl 0976.42020</a></td> </tr><tr> <td>[35]</td> <td class="space">Z. Y. Wang and X. H. Dong, Spectrality of Sierpiński-Moran measures, Monatsh. Math. 195 (2021), 743-761. · <a href="/1469.28010" class="nowrap">Zbl 1469.28010</a></td> </tr><tr> <td>[36]</td> <td class="space">Z.-Y. Wang, J.-C. Liu and X.-H. Dong, On zeros and spectral property of self-affine measures, Nonlinearity 36 (2023), 4187-4208. · <a href="/1519.28008" class="nowrap">Zbl 1519.28008</a></td> </tr><tr> <td>[37]</td> <td class="space">Z.-Y. Wang, J.-C. Liu and J. Su, Spectral property of self-affine measures on R n , J. Fourier Anal. Appl. 27 (2021), no. 5, art. 79, 28 pp. · <a href="/1477.28010" class="nowrap">Zbl 1477.28010</a></td> </tr><tr> <td>[38]</td> <td class="space">Zhi-Yi Wu School of Mathematics and Information Science Guangzhou University Guangzhou, 510006, P. R. China E-mail: zhiyi_wu2021@163.com Min-Min Zhang (corresponding author) Department of Applied Mathematics Anhui University of Technology Ma’anshan, 243002, P. R. China E-mail: zhangminmin0907@163.com Feng-Li Yin School of Mathematics and Statistics Zhoukou Normal University Zhoukou, 466001, P. R. China E-mail: yinfengli05181@163.com</td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. 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