Orthogonal polynomials on the real line (OPRL) were developed in the nineteenth century
and orthogonal polynomials on the unit circle (OPUC) were initially developed around 1920 …

Matrix valued Jacobi polynomials Page 1 Bull. Sci. math. 127 (2003) 207–214 www.elsevier.com/locate/bulsci
Matrix valued Jacobi polynomials F. Alberto Grünbaum1 Department of Mathematics …

Matrix orthogonal Laurent polynomials in the unit circle and the theory of Toda-like
integrable systems are connected using the Gauss–Borel factorization of two, left and a right …

The subject of orthogonal polynomials cuts across a large piece of mathematics and its
applications. Two notable examples are mathematical physics in the 19th and 20th …

Some families of orthogonal matrix polynomials satisfying second-order differential
equations with coefficients independent of n have recently been introduced (see [Internat …

In this paper we prove some characterizations of the matrix orthogonal polynomials whose
derivatives are also orthogonal, which generalize other known ones in the scalar case. In …

In this paper, matrix orthogonal polynomials in the real line are described in terms of a
Riemann–Hilbert problem. This approach provides an easy derivation of discrete equations …

We give an analog of exceptional polynomials in the matrix‐valued setting by considering
suitable factorizations of a given second‐order differential operator and performing Darboux …

We consider a matrix valued version of the bispectral problem involving a block tridiagonal
doubly infinite matrix and a first-order differential operator with matrix coefficients. We give a …

Matrix Szegő biorthogonal polynomials for quasi‐definite matrices of Hölder continuous
weights are studied. A Riemann‐Hilbert problem is uniquely solved in terms of the matrix …