Christoffel transform of classical discrete measures and invariance of determinants of classical and classical discrete polynomials
Given a finite set of complex numbers U and a classical discrete measure μ, we consider the Christoffel transform . Under mild conditions on the finite set U, we show that the orthogonal polynomials with respect to enjoy a bunch of non trivial determinantal representations in terms of the classical...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/182285 |
| Acceso en línea: | https://hdl.handle.net/11441/182285 https://doi.org/10.1016/j.jmaa.2021.125306 |
| Access Level: | acceso abierto |
| Palabra clave: | Christoffel transforms Classical discrete orthogonal polynomials Classical orthogonal polynomials |
| Sumario: | Given a finite set of complex numbers U and a classical discrete measure μ, we consider the Christoffel transform . Under mild conditions on the finite set U, we show that the orthogonal polynomials with respect to enjoy a bunch of non trivial determinantal representations in terms of the classical discrete orthogonal polynomials with respect to μ. Under additional assumptions on the finite set U, we dualize these determinantal representations and find some invariance properties for quasi Casoration determinants whose entries are classical discrete orthogonal polynomials. Passing to the limit we recover some known invariance properties for Wronskian determinant whose entries are classical polynomials. |
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