In a previous paper we have introduced matrixvalued analogues of the Chebyshev polynomials by studying matrix-valued spherical functions on SU(2) × SU(2). In particular the matrix-size of the polynomials is arbitrarily ...

Matrix-valued spherical functions related to the quantum symmetric pair for the quantum analogue of (SU (2) × SU (2) , diag) are introduced and studied in detail. The quantum symmetric pair is given in terms of a quantised ...

A general family of matrix valued Hermite type orthogonal polynomials is introduced as the matrix orthogonal polynomials with respect to a weight. The matrix polynomials are eigenfunctions of a matrix differential equation. ...

We introduce matrix-valued weight functions of arbitrary size, which are analogues of the weight function for the Gegenbauer or ultraspherical polynomials for the parameter ν> 0. The LDU-decomposition of the weight is ...

We extend to a situation involving matrix-valued orthogonal polynomials, a scalar result that originates in work of Shannon and a ground-breaking series of papers by Slepian, Landau and Pollak at Bell Labs in the 1960s. ...

In Part 1 we study the spherical functions on compact symmetric pairs of arbitrary rank under a suitable multiplicity freeness assumption and additional conditions on the branching rules. The spherical functions are taking ...

Using the theory introduced by Casper and Yakimov, we investigate the structure of algebras of differential and difference operators acting on matrix valued orthogonal polynomials (MVOPs) on (Formula presented.), and we ...

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

In this paper, we determine all irreducible spherical functions of any K-type associated to the pair (G;K) = (SO(4); SO(3)). This is accomplished by associating to a vector valued function H = H(u) of a real variable ...

In this paper, we exhibit explicitly a sequence of (Formula presented.) matrix valued orthogonal polynomials with respect to a weight (Formula presented.) , for any pair of real numbers p and n such that (Formula presented.). ...