Poncelet's Theorem, Paraorthogonal Polynomials and the Numerical Range of Compressed Multiplication Operators
Spectral Theory
2021-08-11 v2
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 [11]. 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
Cite
@article{arxiv.1810.13357,
title = {Poncelet's Theorem, Paraorthogonal Polynomials and the Numerical Range of Compressed Multiplication Operators},
author = {Andrei Martinez-Finkelshtein and Brian Simanek and Barry Simon},
journal= {arXiv preprint arXiv:1810.13357},
year = {2021}
}
Comments
46 pages, 4 figures; minor revisions from v1; accepted for publication in Adv. Math