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

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

doi:10.1007/978-3-030-75425-9_8

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

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

^*Corresponding author for this work

Departamento de Física y Matemáticas

Research output: Chapter in Book/Report/Conference proceeding › Chapter

1 Citation (Scopus)

Abstract

This paper deals with sequences of monic polynomials { Φ_n(μ_k;z)}_n≥0, k = 0, 1, orthogonal with respect to two nontrivial Borel measures μ_k, k = 0, 1, supported on the unit circle, satisfying (formula presented) n ≥ 3, where b_n ≠ 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 language	English
Title of host publication	Operator Theory
Subtitle of host publication	Advances and Applications
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	113-142
Number of pages	30
DOIs	https://doi.org/10.1007/978-3-030-75425-9_8
Publication status	Published - 2021

Publication series

Name	Operator Theory: Advances and Applications
Volume	285
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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10.1007/978-3-030-75425-9_8

Cite this

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abstract = "This paper deals with sequences of monic polynomials { Φn(μk;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.",

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An Extension of the Coherent Pair of Measures of the Second Kind on the Unit Circle. / Garza, Lino G.; Marcellán, F.; Ranga, A. Sri.
Operator Theory: Advances and Applications. Springer Science and Business Media Deutschland GmbH, 2021. p. 113-142 (Operator Theory: Advances and Applications; Vol. 285).

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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N1 - 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.

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N2 - This paper deals with sequences of monic polynomials { Φn(μk;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.

AB - This paper deals with sequences of monic polynomials { Φn(μk;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.

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

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