Differential properties of matrix orthogonal polynomials

Abstract

In this paper a general theory of semi-classical matrix orthogonal polynomials is developed. We define the semi-classical linear functionals by means of a distributional equation $D(uA)=uB,$ where $A$ and $B$ are matrix polynomials. Several characterizations for these semi-classical functionals are given in terms of the corresponding (left) matrix orthogonal polynomials sequence. They involve a quasi-orthogonality property for their derivatives, a structure relation and a second order differo-differential equation. Finally we illustrate the preceding results with some non-trivial examples.

23 pages

Cited by in corpus (7)

• The Analytic Theory of Matrix Orthogonal Polynomials
• Matrix Orthogonal Laurent Polynomials on the Unit Circle and Toda Type Integrable Systems
• Riemann--Hilbert problems, matrix orthogonal polynomials and discrete matrix equations with singularity confinement
• Ladder relations for a class of matrix valued orthogonal polynomials
• Singular examples of the Matrix Bochner Problem
• Matrix biorthogonal polynomials in the unit circle: Riemann-Hilbert problem and matrix discrete Painleve II system
• Matrix orthogonal polynomials whose derivatives are also orthogonal