Matrix-valued bispectral discrete orthogonal polynomials

Abstract

We develop a unified construction of matrix-valued orthogonal polynomials associated with discrete weights, yielding bispectral sequences as eigenfunctions of second-order difference operators. This general framework extends the discrete families in the classical Askey scheme to the matrix setting by producing explicit matrix analogues of the Krawtchouk, Hahn, Meixner, and Charlier polynomials. Our results include explicit expressions for the weights, the orthogonal polynomials, and the corresponding difference operators.

16 pages