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Published June 20, 2019 | Accepted Version
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Poncelet's theorem, paraorthogonal polynomials and the numerical range of compressed multiplication operators

Martínez–Finkelshtein, Andrei
Simanek, Brian
Simon, Barry ORCID icon
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Abstract

There has been considerable recent literature connecting Poncelet's theorem to ellipses, Blaschke products and numerical ranges, summarized, for example, in the recent book [16]. We show how those results can be understood using ideas from the theory of orthogonal polynomials on the unit circle (OPUC) and, in turn, can provide new insights to the theory of OPUC.

Additional Information

© 2019 Elsevier. Received 31 October 2018, Revised 27 March 2019, Accepted 7 April 2019, Available online 30 April 2019. Communicated by D. Stroock. Research supported in part by the Spanish Government and the European Regional Development Fund (grant MTM2017-89941-P), Junta de Andalucía (research group FQM-229 and Instituto Interuniversitario Carlos I de Física Teórica y Computacional), and by the University of Almería (Campus de Excelencia Internacional del Mar CEIMAR). Research supported in part by NSF grant DMS-1665526 and in part by Israeli BSF Grant No. 2014337. B.S. would like to thank Fritz Gesztesy and Lance Littlejohn for the invitation to visit Baylor where our collaboration was begun.

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