Document Zbl 1526.35311

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Geom. Anal.</a> <a href="/?q=in%3A503214" title="Articles in this Issue">33, No. 12, Paper No. 375, 23 p. (2023)</a>. </div> <div class="abstract">Summary: Consider a fractional operator $P^s, 0<s<1$, for connection Laplacian $P:=\nabla^* \nabla +A$ on a smooth Hermitian vector bundle over a closed, connected Riemannian manifold of dimension $n\geq 2$. We show that local knowledge of the metric, Hermitian bundle, connection, potential, and source-to-solution map associated with $P^s$ determines these structures globally. This extends a result known for the fractional Laplace-Beltrami operator.</div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A35R30" title="MSC2020">35R30</a> </td> <td class="space"> Inverse problems for PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35R11" title="MSC2020">35R11</a> </td> <td class="space"> Fractional partial differential equations </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A58J05" title="MSC2020">58J05</a> </td> <td class="space"> Elliptic equations on manifolds, general theory </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Ainverse+problem">inverse problem</a>; <a href="/?q=ut%3Afractional+Laplacian">fractional Laplacian</a>; <a href="/?q=ut%3ACalderon+problem">Calderon problem</a>; <a href="/?q=ut%3Aconnection+Laplacian">connection Laplacian</a>; <a href="/?q=ut%3Abundle+Laplacian">bundle Laplacian</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 1526.35311" data-ciurl="/ci/07754894" data-biburl="/bibtex/07754894.bib" data-amsurl="/amsrefs/07754894.bib" data-xmlurl="/xml/07754894.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07754894.pdf" title="Zbl 1526.35311 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/10.1007/s12220-023-01426-3" aria-label="DOI for “An inverse problem for fractional connection Laplacians”" title="10.1007/s12220-023-01426-3">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2208.00454"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">Albin, P.; Guillarmou, C.; Tzou, L.; Uhlmann, G., Inverse boundary problems for systems in two dimensions, Ann. 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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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