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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Bibliographic Details
Published in:arXiv.org 2015-06
Main Authors: Grünbaum, F Alberto, Pacharoni, Inés, Zurrián, Ignacio Nahuel
Format: Article
Language:English
Subjects:
Constraining
Functions (mathematics)
Information theory
Mathematical analysis
Matrix methods
Operators (mathematics)
Polynomials
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1410.1232