A class of Sobolev orthogonal polynomials on the unit circle and associated continuous dual Hahn polynomials: Bounds, asymptotics and zeros

Autor(es)

Bracciali, Cleonice F. ^[1] ; da Silva, V, Jessica ; Ranga, A. Sri ^[2]

Afiliação do(s) autor(es)

^[1] UNESP Univ Estadual Paulista, IBILCE, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil

^[2] da Silva, Jessica, V, UNESP Univ Estadual Paulista, IBILCE, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Approximation Theory; v. 268, AUG 2021.
• Citações Web of Science: 0

Resumo

This paper deals with orthogonal polynomials and associated connection coefficients with respect to a class of Sobolev inner products on the unit circle. Under certain conditions on the parameters in the inner product it is shown that the connection coefficients are related to a subfamily of the continuous dual Hahn polynomials. Properties regarding bounds and asymptotics are also established with respect to these parameters. Criteria for knowing when the zeros of the (Sobolev) orthogonal polynomials and also the zeros of their derivatives stay within the unit disk have also been addressed. By numerical experiments some further information on the parameters is also found so that the zeros remain within the unit disk. (C) 2021 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 20/14244-2 - Polinômios ortogonais e estudos relacionados
• Beneficiário: Alagacone Sri Ranga
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 16/09906-0 - Análise harmônica, teoria da aproximação, funções especiais e aplicações
• Beneficiário: Dimitar Kolev Dimitrov
• Modalidade de apoio: Auxílio à Pesquisa - Temático