Invariance properties of Wronskian type determinants of classical and classical discrete orthogonal polynomials☆

Given a finite set of nonnegative integers (written in increasing order of magnitude) and a classical discrete family of orthogonal polynomials (Charlier, Meixner, Krawtchouk or Hahn), we consider the Casorati determinant . In this paper we prove an invariance property of this kind of Casorati deter...

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Detalles Bibliográficos
Autores: Curbera Costello, Guillermo, Durán Guardeño, Antonio José
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2019
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/179369
Acceso en línea:https://hdl.handle.net/11441/179369
https://doi.org/10.1016/j.jmaa.2019.01.078
Access Level:acceso abierto
Palabra clave:Charlier polynomials
Hermite polynomials
Meixner polynomials
Laguerre polynomials
Hahn polynomials
Jacobi polynomials
Descripción
Sumario:Given a finite set of nonnegative integers (written in increasing order of magnitude) and a classical discrete family of orthogonal polynomials (Charlier, Meixner, Krawtchouk or Hahn), we consider the Casorati determinant . In this paper we prove an invariance property of this kind of Casorati determinants when the set F is substituted by the set . Our approach uses orthogonal polynomials that are eigenfunctions of higher order difference operators (Krall discrete polynomials). These polynomials are orthogonal with respect to certain Christoffel transforms of the classical discrete measures. By passing to the limit, this invariance property is extended to Wronskian type determinants whose entries are Hermite, Laguerre and Jacobi polynomials.