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...
| Autores: | , |
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| 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 |
| 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. |
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