Time and Band Limiting for Matrix Valued Functions

GRÜNBAUM ALBERTO; PACHARAONI INÉS; ZURRIÁN IGNACIO

SYMMETRY, INTEGRABILITY AND GEOMETRY

NATL ACAD SCI UKRAINE

Año: 2015

1815-0659

The main purpose of this paper is to extend toa situation involving matrix valued orthogonal polynomials and spherical functions a result that traces its origin and its importance to work of Claude Shannon in lying the mathematicalfoundations 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.