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Orthogonal Polynomials Associated with Complementary Chain Sequences

Orthogonal Polynomials Associated with Complementary Chain Sequences

Using the minimal parameter sequence of a given chain sequence, we introduce the concept of complementary chain sequences, which we view as perturbations of chain sequences. Using the relation between these complementary chain sequences and the corresponding Verblunsky coefficients, the para-orthogo...

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Main Authors: Behera, K.K., Sri Ranga, A., Swaminathan, A.
Format: Article
Language:English
Published: Інститут математики НАН України 2016
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/147841
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spelling irk-123456789-1478412019-02-17T01:26:49Z Orthogonal Polynomials Associated with Complementary Chain Sequences Behera, K.K. Sri Ranga, A. Swaminathan, A. Using the minimal parameter sequence of a given chain sequence, we introduce the concept of complementary chain sequences, which we view as perturbations of chain sequences. Using the relation between these complementary chain sequences and the corresponding Verblunsky coefficients, the para-orthogonal polynomials and the associated Szegő polynomials are analyzed. Two illustrations, one involving Gaussian hypergeometric functions and the other involving Carathéodory functions are also provided. A connection between these two illustrations by means of complementary chain sequences is also observed. 2016 Article Orthogonal Polynomials Associated with Complementary Chain Sequences / K.K. Behera, A. Sri Ranga, A. Swaminathan // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 27 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 42C05; 33C45; 30B70 DOI:10.3842/SIGMA.2016.075 http://dspace.nbuv.gov.ua/handle/123456789/147841 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description Using the minimal parameter sequence of a given chain sequence, we introduce the concept of complementary chain sequences, which we view as perturbations of chain sequences. Using the relation between these complementary chain sequences and the corresponding Verblunsky coefficients, the para-orthogonal polynomials and the associated Szegő polynomials are analyzed. Two illustrations, one involving Gaussian hypergeometric functions and the other involving Carathéodory functions are also provided. A connection between these two illustrations by means of complementary chain sequences is also observed.
format Article
author Behera, K.K.
Sri Ranga, A.
Swaminathan, A.
spellingShingle Behera, K.K.
Sri Ranga, A.
Swaminathan, A.
Orthogonal Polynomials Associated with Complementary Chain Sequences
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Behera, K.K.
Sri Ranga, A.
Swaminathan, A.
author_sort Behera, K.K.
title Orthogonal Polynomials Associated with Complementary Chain Sequences
title_short Orthogonal Polynomials Associated with Complementary Chain Sequences
title_full Orthogonal Polynomials Associated with Complementary Chain Sequences
title_fullStr Orthogonal Polynomials Associated with Complementary Chain Sequences
title_full_unstemmed Orthogonal Polynomials Associated with Complementary Chain Sequences
title_sort orthogonal polynomials associated with complementary chain sequences
publisher Інститут математики НАН України
publishDate 2016
url http://dspace.nbuv.gov.ua/handle/123456789/147841
citation_txt Orthogonal Polynomials Associated with Complementary Chain Sequences / K.K. Behera, A. Sri Ranga, A. Swaminathan // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 27 назв. — англ.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT beherakk orthogonalpolynomialsassociatedwithcomplementarychainsequences
AT srirangaa orthogonalpolynomialsassociatedwithcomplementarychainsequences
AT swaminathana orthogonalpolynomialsassociatedwithcomplementarychainsequences
first_indexed 2023-05-20T17:28:39Z
last_indexed 2023-05-20T17:28:39Z
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