Matrix valued orthogonal polynomials arising from the complex projective space

I. PACHARONI, J. TIRAO

CONSTRUCTIVE APPROXIMATION

Springer Verlag

Lugar: Nueva York; Año: 2006

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 canconsider the corresponding 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 associatedto the pair (SU(n+1), U(n)) we obtain new families of such pair {W,D}. These depend on enough integer parameters to obtain an immediate extension beyond these cases.