Time and Band Limiting for Matrix Valued Functions, an Example
Spectral Theory
2015-06-15 v3
Abstract
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.
Cite
@article{arxiv.1410.1232,
title = {Time and Band Limiting for Matrix Valued Functions, an Example},
author = {F. Alberto Grünbaum and Inés Pacharoni and Ignacio Nahuel Zurrián},
journal= {arXiv preprint arXiv:1410.1232},
year = {2015}
}