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

  • Lino G. Garza
    ,
  • F. Marcellán(corresponding author)
    ,
  • A. Sri Ranga
*Corresponding author for this work
Research Output:
Chapter in Book/Report/Conference proceeding
Chapter

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FWCI
0.90
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Author count
3
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Paper percentile
68
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Citations
1
Scopus
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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.

Publication Information

Output type

Research Output:
Chapter in Book/Report/Conference proceeding
Chapter

Host publication Subtitle

Advances and Applications

Original language

English

Pages from-to (Number of pages)

Pages 113-142 (30 pages)

Publication milestones

  • Published - 2021

Publication status

Published - 2021

Publisher

Springer Science and Business Media Deutschland GmbH, Germany

Publication series

  • Publication series name: Operator Theory: Advances and Applications
    ISSN (Print): 0255-0156
    ISSN (Electronic): 2296-4878
    Volume: 285

Publication IDs

  • Scopus: 85119148227

Host publication title

Operator Theory

Access to documents

Funding Details

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. 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. 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).
FundersFunding numbers
FAPESP
-
CNPq
2016/09906-0
UC3M
MTM2015–65888-C4-2-P
ERDF
304087/2018-1
MINECO
PGC2018-096504-B-C33
AEI
-