Ladder relations for a class of matrix valued orthogonal polynomials

2019/07/31 by Alfredo Deaño, Bruno Eijsvoogel, Pablo Román
Computer Science · Mathematics · Physics and Astronomy · #Algebra over a field #Classical orthogonal polynomials #Constant coefficients #Differential (mechanical device) #Differential equation #Geometry #Mathematical analysis #Mathematical functions and polynomials #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Matrix polynomial #Nonlinear Waves and Solitons #Orthogonal polynomials #Physics #Polynomial #Polynomial matrix #Pure mathematics #Scalar (mathematics) #math.CA

paper · pdf · doi:10.1111/sapm.12351

openalex publication_date 2020/11/11 · arxiv created 2020/11/16 · arxiv updated 2020/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

Abstract 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 , 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 on the real line, where is a scalar polynomial of even degree with positive leading coefficient and is a constant matrix.

Citations

• Differential properties of matrix orthogonal polynomials
• Lectures on random matrix models. The Riemann-Hilbert approach
• Ladder operators and differential equations for orthogonal polynomials
• Orthogonal polynomials and their derivatives, I
• Classical and Quantum Orthogonal Polynomials in One Variable