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French summary)</i> <a class="label nowrap" href="/1364.42011">Zbl 1364.42011</a> </h2> <div class="source"> <a href="/serials/1597" title="Journal Profile">J. Math. Pures Appl. (9)</a> <a href="/?q=in%3A362528" title="Articles in this Issue">107, No. 2, 183-204 (2017)</a>. </div> <div class="abstract">The authors summarize the contents of this paper in the abstract as follows: We study spectral measures generated by infinite convolution products of discrete measures generated by Hadamard triples, and we present sufficient conditions for the measures to be spectral, generalizing a criterion by Strichartz. We then study the spectral measures generated by random convolutions of finite atomic measures and rescaling, where the digits are chosen from a finite collection of digit sets. We show that in dimension one, or in higher dimensions under certain conditions, “almost all” such measures generate spectral measures, or, in the case of complete digit sets, translational tiles. Our proofs are based on the study of self-affine spectral measures and tiles generated by Hadamard triples in quasi-product form.<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A9741">Kun Soo Chang (Seoul)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6677813">Cited in <strong>34</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A42B10" title="MSC2020">42B10</a> </td> <td class="space"> Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type </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%3A42C30" title="MSC2020">42C30</a> </td> <td class="space"> Completeness of sets of functions in nontrigonometric harmonic analysis </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aspectral+measure">spectral measure</a>; <a href="/?q=ut%3Ainfinite+convolution">infinite convolution</a>; <a href="/?q=ut%3Atile">tile</a>; <a href="/?q=ut%3Aself-affine">self-affine</a></div> <!-- Modal used to show zbmath metadata in different output formats--> <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;"> <!-- alert for connection errors etc --> </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"> <!-- Button trigger metadata modal --> <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1364.42011" data-ciurl="/ci/06677813" data-biburl="/bibtex/06677813.bib" data-amsurl="/amsrefs/06677813.bib" data-xmlurl="/xml/06677813.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06677813.pdf" title="Zbl 1364.42011 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/10.1016/j.matpur.2016.06.003" aria-label="DOI for “Spectral measures generated by arbitrary and random convolutions”" title="10.1016/j.matpur.2016.06.003">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/1509.04511"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">An, Li-Xiang; He, Xing-Gang; Lau, Ka-Sing, Spectrality of a class of infinite convolutions, Adv. 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