Time and Band Limiting for Matrix Valued Functions, an Example

PACHARONI, I. ; ZURRIAN, I.; GRUNBAUM, F:A

SYMMETRY, INTEGRABILITY AND GEOMETRY

NATL ACAD SCI UKRAINE

Año: 2015 vol. 11 p. 1 - 14

1815-0659

The main purpose of this paper is to extend to a situation involving matrixvalued orthogonal polynomials and spherical functions, a result that traces its origin and itsimportance to work of Claude Shannon in laying the mathematical foundations of informationtheory 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 bispectralproperty implies that the corresponding global operator of ?time and band limiting?admits a commuting local operator. This is a noncommutative analog of the famous prolatespheroidal wave operator.