A Sequence of Matrix Valued Orthogonal Polynomials Associated to Spherical Functions

P. ROMÁN

Madrid

Workshop; International Workshop on Orthogonal Polynomials and Approximation Theory 2008; 2008

Universidad Carlos III

Abstract: In this talk we exhibit an explicit expression of a family of matrix valued orthogonalpolynomials {Pn}n with respect to a weight W, that are eigenfunctions of a second-order orderdifferential operator D. The weight W and the differential operator W were found by Pacharoniand Tirao in 2006, using some aspects of the theory of the spherical functions associated to thecomplex projective spaces. We also find other second-order differential operator E symmetricwith respect to W and we describe the algebra generated by D and E. These results are part of ajoint work with I. Pacharoni: A Sequence of Matrix Valued Orthogonal Polynomials Associatedto Spherical Functions, Constructive Approximation, 2007.