Poncelet's theorem, paraorthogonal polynomials and the numerical range of compressed multiplication operators

Andrei Martínez–Finkelshtein; Brian Simanek; Barry Simon

doi:10.1016/j.aim.2019.04.027

Poncelet's theorem, paraorthogonal polynomials and the numerical range of compressed multiplication operators

Andrei Martínez–Finkelshtein, Brian Simanek, Barry Simon

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

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.

Original language	English
Pages (from-to)	992-1035
Number of pages	44
Journal	Advances in Mathematics
Volume	349
DOIs	https://doi.org/10.1016/j.aim.2019.04.027
State	Published - 20 Jun 2019
Externally published	Yes

Keywords

Blaschke products
Numerical range
OPUC
POPUC
Poncelet's theorem

ASJC Scopus subject areas

General Mathematics

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10.1016/j.aim.2019.04.027

Cite this

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title = "Poncelet's theorem, paraorthogonal polynomials and the numerical range of compressed multiplication operators",

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.",

keywords = "Blaschke products, Numerical range, OPUC, POPUC, Poncelet's theorem",

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AU - Martínez–Finkelshtein, Andrei

AU - Simanek, Brian

AU - Simon, Barry

PY - 2019/6/20

Y1 - 2019/6/20

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AB - 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.

KW - Blaschke products

KW - Numerical range

KW - OPUC

KW - POPUC

KW - Poncelet's theorem

UR - https://www.scopus.com/pages/publications/85064907484

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ER -

Poncelet's theorem, paraorthogonal polynomials and the numerical range of compressed multiplication operators

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

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