Time-and-band limiting for matrix-valued orthogonal polynomials related with 2 × 2 hypergeometric operators
We consider a family of matrix-valued orthogonal polynomials of size 2 × 2, which are common eigenfunctions of a differential operator of hypergeometric type, in connection with the problem of time-and-band limiting. The problem in question is as follows: given a global operator, defined by an integ...
| Autores: | , , |
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| Tipo de recurso: | capítulo de libro |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/167311 |
| Acceso en línea: | https://hdl.handle.net/11441/167311 https://doi.org/10.1090/conm/807/16164 |
| Access Level: | acceso abierto |
| Palabra clave: | Time-band limiting Matrix valued orthogonal polynomials |
| Sumario: | We consider a family of matrix-valued orthogonal polynomials of size 2 × 2, which are common eigenfunctions of a differential operator of hypergeometric type, in connection with the problem of time-and-band limiting. The problem in question is as follows: given a global operator, defined by an integral kernel or a full matrix, one looks for a local operator given by a second order differential operator or a block tridiagonal matrix respectively, commuting with the global one. We apply the techniques for the construction of the commuting local operator introduced in a previous work by A. Gr¨unbaum, I. Pacharoni and I. Zurrian in the matrix-valued setting, where the role of bispectrality is crucial. This constitutes an illustrative example of an extension to a situation involving matrix orthogonality, of a scalar result that originates in a series of papers by D. Slepian, H. Landau and H. Pollak at Bell Labs in the sixties. |
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