Castro Smirnova, Mirta MaríaFoulquié Moreno, AnaFradi, A.2025-01-232025-01-232024Castro Smirnova, M.M., Foulquié Moreno, A. y Fradi, A. (2024). Time-and-band limiting for matrix-valued orthogonal polynomials related with 2 × 2 hypergeometric operators. En Recent Progress in Special Functions .Rhode Island, USA: American Mathematical Society.97814704742949781470477226https://hdl.handle.net/11441/167311We 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.application/pdf21 p.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Time-band limitingMatrix valued orthogonal polynomialsinfo:eu-repo/semantics/bookPartinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1090/conm/807/16164