Matrix polynomials orthogonal with respect to a non-symmetric matrix of measures

Abstract

The paper focuses on matrix-valued polynomials satisfying a three-term recurrence relation with constant matrix coefficients. It is shown that they form an orthogonal system with respect to a matrix of measures, not necessarily symmetric. Moreover, it is stated the condition on the coefficients of the recurrence formula for which the matrix measure is symmetric.

Keywords

• matrix orthogonal polynomials
• recurrence formula
• matrix of measures
• block Jacobi matrices