An Extension of the Coherent Pair of Measures of the Second Kind on the Unit Circle

Lino G. Garza, F. Marcellán, A. Sri Ranga

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

This paper deals with sequences of monic polynomials { Φnk;z)}n≥0, k = 0, 1, orthogonal with respect to two nontrivial Borel measures μk, k = 0, 1, supported on the unit circle, satisfying (formula presented) n ≥ 3, where bn ≠ 0. We find examples of pairs of measures (μ0, μ1) for which this property holds. The analysis of polynomials orthogonal with respect to the Sobolev inner product associated with the pair of measures (μ0, μ1) is presented. Some properties concerning their connection coefficients are given.

Original languageEnglish
Title of host publicationOperator Theory
Subtitle of host publicationAdvances and Applications
PublisherSpringer Science and Business Media Deutschland GmbH
Pages113-142
Number of pages30
DOIs
Publication statusPublished - 2021

Publication series

NameOperator Theory: Advances and Applications
Volume285
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

Bibliographical note

Funding Information:
This work was done as a part of the doctoral thesis of the author Lino G. Garza at Universidad Carlos III de Madrid, Spain, supervised by Francisco Marcellán and supported by the grant MTM2015–65888-C4-2-P, Ministerio de Economía, Industria y Competitividad of Spain.

Funding Information:
The research of the author A. Sri Ranga was supported by the grant 304087/2018-1 from CNPq of Brazil and by the grant 2016/09906-0 from FAPESP of the state of São Paulo, Brazil.

Funding Information:
The research of the author Francisco Marcellán was supported by the grant PGC2018-096504-B-C33 from the Agencia Estatal de Investigación (AEI) of Spain and Fondo Europeo de Desarrollo Regional (FEDER).

Publisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

All Science Journal Classification (ASJC) codes

  • Analysis

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