Time and band limiting for matrix valued functions, an example

The main purpose of this paper is to extend to a situation involving matrix valued orthogonal polynomials and spherical functions, a result that traces its origin and its importance to work of Claude Shannon in laying the mathematical foundations of information theory and to a remarkable series of p...

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Detalles Bibliográficos
Autores principales: Grünbaum, Francisco Alberto, Pacharoni, María Inés, Zurrián, Ignacio Nahuel
Formato: article
Lenguaje:Inglés
Publicado: 2022
Materias:
Acceso en línea:http://hdl.handle.net/11086/22154
https://doi.org/10.3842/SIGMA.2015.044
Aporte de:Repositorio Digital Universitario (UNC) de Universidad Nacional de Córdoba Ver origen
Descripción
Sumario:The main purpose of this paper is to extend to a situation involving matrix valued orthogonal polynomials and spherical functions, a result that traces its origin and its importance to work of Claude Shannon in laying the mathematical foundations of information theory and to a remarkable series of papers by D. Slepian, H. Landau and H. Pollak. To our knowledge, this is the first example showing in a non-commutative setup that a bispectral property implies that the corresponding global operator of “time and band limiting” admits a commuting local operator. This is a noncommutative analog of the famous prolate spheroidal wave operator.