scientific article; zbMATH DE number 2211575

DOI10.1155/IMRN.2005.1371zbMath1102.42013OpenAlexW2516240294MaRDI QIDQ5694420

Antonio J. Duran, F. Alberto Gruenbaum

Publication date: 30 September 2005

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/imrn.2005.1371

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zbMATH Keywords

orthogonal matrix polynomialssecond order differential equationsweight matricesBochner characterization

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Matrix equations and identities (15A24) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30) Other special orthogonal polynomials and functions (33C47)

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Matrix Gegenbauer polynomials: the \(2\times 2\) fundamental cases ⋮ Matrix orthogonal polynomials whose derivatives are also orthogonal ⋮ Pre-sequences of matrix orthogonal polynomials ⋮ Relative asymptotics of matrix orthogonal polynomials for Uvarov perturbations: the degenerate case ⋮ Asymptotics of matrix valued orthogonal polynomials on \([-1, 1\)] ⋮ On \(q\)-special matrix functions using quantum algebraic techniques ⋮ On the Hahn's property for matrix orthogonal polynomials on the unit circle ⋮ Matrix orthogonal polynomials satisfying second-order differential equations: coping without help from group representation theory ⋮ Reducibility of matrix weights ⋮ Rodrigues's Formulas for Orthogonal Matrix Polynomials Satisfying Higher-Order Differential Equations ⋮ A method to find weight matrices having symmetric second-order differential operators with matrix leading coefficient ⋮ Generating orthogonal matrix polynomials satisfying second order differential equations from a trio of triangular matrices ⋮ Matrix valued orthogonal polynomials of Jacobi type: the role of group representation theory.

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