Properties of Matrix Orthogonal Polynomials via their Riemann-Hilbert Characterization

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2011
• Main Authors: Grünbaum, F.A., de la Iglesia, M.D., Martínez-Finkelshtein, A.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2011
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147659
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Properties of Matrix Orthogonal Polynomials via their Riemann-Hilbert Characterization / F.A. Grünbaum, M.D. de la Iglesia, A. Martínez-Finkelshtein // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 52 назв. — англ.

We give a Riemann-Hilbert approach to the theory of matrix orthogonal polynomials. We will focus on the algebraic aspects of the problem, obtaining difference and differential relations satisfied by the corresponding orthogonal polynomials. We will show that in the matrix case there is some extra fr...