A class of Sobolev orthogonal polynomials on the unit circle and associated continuous dual Hahn polynomials: Bounds, asymptotics and zeros
Nenhuma Miniatura disponível
Data
2021-08-01
Autores
Bracciali, Cleonice F. [UNESP]
da Silva, Jéssica V. [UNESP]
Sri Ranga, A. [UNESP]
Título da Revista
ISSN da Revista
Título de Volume
Editor
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.
Descrição
Palavras-chave
Circular Jacobi polynomials, Continuous dual Hahn polynomials, Sobolev orthogonal polynomials on the unit circle
Como citar
Journal of Approximation Theory, v. 268.