Ladder relations for a class of matrix valued orthogonal polynomials

DEAÑO, ALFREDO; EIJSVOOGEL, BRUNO; ROMÁN, PABLO

STUDIES IN APPLIED MATHEMATICS

WILEY-BLACKWELL PUBLISHING, INC

Año: 2020

0022-2526

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 R, and we derive algebraic and differential relations for these MVOPs. A particular case of importance is that of MVOPs with respect to a matrix weight of the form W(x)=e^(-v(x)) e^(xA)e^(xA^*) on the real line, where v(x) is a scalar polynomial of even degree with positive leading coefficient and A is a constant matrix.