Pastro polynomials and Sobolev-type orthogonal polynomials on the unit circle based on a q-difference operator

ABSTRACT

Applications of orthogonal polynomials on the unit circle have attracted the attention of many researchers in recent years. Pastro polynomials, which are basic hypergeometric polynomials, are known to be biorthogonal polynomials on the unit circle. However, with special choice of parameters they provide one of the nicest examples of orthogonal polynomials on the unit circle. Our objective here is to consider some properties of three sequences of polynomials which are related to these Pastro orthogonal polynomials on the unit circle by a q-difference operator. We also provide information regarding connection formulas, bounds for the connection coefficients as well as outer relative asymptotics associated with these sequences of polynomials.

KEYWORDS:

• Orthogonal polynomials on the unit circle
• Sobolev-type orthogonal polynomials on the unit circle
• connection formulas
• Pastro polynomials

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• Primary 33D15
• 42C05
• Secondary33D45

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is part of the doctoral thesis of the author Mijael Hancco Suni at IBILCE/UNESP, São José do Rio Preto, SP, Brazil, supported by a grant from CAPES, Brazil. However, this work was completed while he was visiting Francisco Marcellán at the Department of Mathematics of Universidad Carlos III de Madrid (UC3M). His stay in UC3M, for a period of one year during 2021-2022, was supported by doctoral sandwich students grants 88887.570304/2020-00 from the program CAPES/PrInt of Brazil. This author is extremely grateful to UC3M for receiving all the necessary support for this research. The research of the author Francisco Marcellán was supported by the grant 88887.575061/2020-00 (PrInt) from CAPES of Brazil, by FEDER/Ministerio de Ciencia e Innovación-Agencia Estatal de Investigación of Spain, grant PID2021-122154NB-I00, PGC2018-096504-B-C33, and the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors, grant EPUC3M23 in the context of the V PRICIT (Regional Program of Research and Technological Innovation) The research of the author Alagacone Sri Ranga was supported by the grant 304087/2018-1 from CNPq of Brazil, by the grant 88887.310463/2018-00 (PRINT) from CAPES of Brazil and by the grant 2020/14244-2 from FAPESP of the state of São Paulo, Brazil.