Matrix valued orthogonal polynomials arising from the complex projective space

PACHARONI, I. AND TIRAO, JUAN

CONSTRUCTIVE APPROXIMATION

Springer Science+Business Media, Inc.

Año: 2007 vol. 25 p. 177 - 192

0176-4276

The main purpose of this paper is to display new families of matrix valued orthogonal polynomials satisfying second order differential equations, obtained from the representation theory of U(n). Given an arbitrary positive definite weight matrix W(t) one can consider sequences matrix valued orthogonal polynomials. These polynomials will be eigenfunctions of some symmetric second order differential operator D only for very special choices of W(t). Starting from the theory of spherical functions associated to the pair S(U(n+1), U(n))  we obtain new families of such pairs {W,D}. These depend on enough integer parameters to obtain an immediate extension beyond these cases.