TIME AND BAND LIMITING FOR MATRIX VALUED FUNCTIONS

IGNACIO N. ZURRIÁN; GRÜNBAUM ALBERTO; INÉS PACHARONI

Congreso; XVIII International Congress on Mathematical Physics - Young Researchers Symposium; 2015

The main purpose of this paper is to extend to a situation involving matrixvalued orthogonal polynomials and spherical functions, a result that tracesits origin and its importance to work of Claude Shannon in laying the math-ematical foundations of information theory and to a remarkable series ofpapers by D. Slepian, H. Landau and H. Pollak. To our knowledge, thisis the rst example showing in a non-commutative setup that a bispectralproperty implies that the corresponding global operator of time and bandlimiting" admits a commuting local operator. This is a noncommutativeanalog of the famous prolate spheroidal wave operator.