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

Author(s)

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

Affiliation

^[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

• Document type: Journal article
• Source: Journal of Approximation Theory; v. 268, AUG 2021.
• Web of Science Citations: 0

Abstract

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)

• FAPESP's process: 20/14244-2 - Orthogonal polynomials and related studies
• Grantee: Alagacone Sri Ranga
• Support Opportunities: Regular Research Grants
• FAPESP's process: 16/09906-0 - Harmonic analysis, approximation theory and applications
• Grantee: Dimitar Kolev Dimitrov
• Support Opportunities: Research Projects - Thematic Grants