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.
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 | |
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