Orthogonal polynomials and perturbations on measures supported on the real line and on the unit circle. A matrix perspective

Luis E. Garza*, Francisco Marcellán

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

The connection between measures supported on the real line (resp. on the unit circle), Hankel (resp. Toeplitz) matrices, Jacobi (resp. Hessenberg and CMV) matrices, Stieltjes (resp. Carathéodory) functions constitutes a key element in the analysis of orthogonal polynomials on the real line (resp. on the unit circle). In the present contribution, we focus our attention on perturbations of the measures supported either on the real line or the unit circle and their consequences on the behavior of the corresponding sequences of orthogonal polynomials and the matrices associated with the multiplication operator in terms on those polynomial bases. The matrix perspective related to such perturbations from the point of view of factorizations (LU and QR) is emphasized. Finally, we show the role of spectral transformations in the analysis of some integrable systems.

Original languageEnglish
Pages (from-to)287-326
Number of pages40
JournalExpositiones Mathematicae
Volume34
Issue number3
DOIs
Publication statusPublished - 2016
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2015 Elsevier GmbH

All Science Journal Classification (ASJC) codes

  • General Mathematics

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