Document Zbl 1491.35472

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Am. Math. Soc.</a> <a href="/?q=in%3A483120" title="Articles in this Issue">150, No. 7, 2849-2860 (2022)</a>. </div> <div class="abstract">Summary: The minimal operator and the maximal operator of an elliptic pseudo-differential operator with symbols on $\mathbb{Z}^n\times\mathbb{T}^n$ are proved to coincide and the domain is given in terms of a Sobolev space. Ellipticity and Fredholmness are proved to be equivalent for pseudo-differential operators on $\mathbb{Z}^n$. The index of an elliptic pseudo-differential operator on $\mathbb{Z}^n$ is also computed.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7541828">Cited in <strong>7</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A35S05" title="MSC2020">35S05</a> </td> <td class="space"> Pseudodifferential operators as generalizations of partial differential operators </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A47G30" title="MSC2020">47G30</a> </td> <td class="space"> Pseudodifferential operators </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A43A85" title="MSC2020">43A85</a> </td> <td class="space"> Harmonic analysis on homogeneous spaces </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A43A77" title="MSC2020">43A77</a> </td> <td class="space"> Harmonic analysis on general compact groups </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aminimal+and+maximal+operators">minimal and maximal operators</a>; <a href="/?q=ut%3Aellipticity">ellipticity</a>; <a href="/?q=ut%3AFredholmness">Fredholmness</a>; <a href="/?q=ut%3Aindex">index</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 1491.35472" data-ciurl="/ci/07541828" data-biburl="/bibtex/07541828.bib" data-amsurl="/amsrefs/07541828.bib" data-xmlurl="/xml/07541828.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07541828.pdf" title="Zbl 1491.35472 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/10.1090/proc/15661" aria-label="DOI for “Ellipticity and Fredholmness of pseudo-differential operators on $\ell^2(\mathbb{Z}^n)$”" title="10.1090/proc/15661">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/1910.05582"title="Note: arXiv document may differ from published version">arXiv</a> <a class="btn btn-default btn-xs" type="button" href="https://biblio.ugent.be/publication/8713876/file/8713878" title="Full Text Link">Link</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Atkinson, F. 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