Matrix orthogonal polynomials satisfying second-order differential equations: coping without help from group representation theory

DOI10.1016/J.JAT.2007.02.003zbMath1221.42046OpenAlexW2057300935MaRDI QIDQ2456670

Antonio J. Duran, F. Alberto Gruenbaum

Publication date: 19 October 2007

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2007.02.003

zbMATH Keywords

differential operatormatrix orthogonality

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Matrix equations and identities (15A24) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30)

Related Items (12)

Orthogonal matrix polynomials satisfying differential equations with recurrence coefficients having non-scalar limits ⋮ Orthogonal matrix polynomials satisfying second order difference equations ⋮ Matrix bispectrality and noncommutative algebras: beyond the prolate spheroidals ⋮ On \(q\)-special matrix functions using quantum algebraic techniques ⋮ The algebra of difference operators associated to a family of orthogonal polynomials ⋮ Rodrigues's Formulas for Orthogonal Matrix Polynomials Satisfying Higher-Order Differential Equations ⋮ Some examples of matrix-valued orthogonal functions having a differential and an integral operator as eigenfunctions ⋮ A method to find weight matrices having symmetric second-order differential operators with matrix leading coefficient ⋮ Constructing orthogonal matrix polynomials satisfying differential equations from two different Laguerre weights ⋮ Generating orthogonal matrix polynomials satisfying second order differential equations from a trio of triangular matrices ⋮ Matrix-valued polynomials generated by the scalar-type Rodrigues' formulas ⋮ Structural formulas for matrix-valued orthogonal polynomials related to \(2\times 2\) hypergeometric operators

Cites Work

• Orthogonal matrix polynomials, scalar-type Rodrigues formulas and Pearson equations
• Ratio asymptotics for orthogonal matrix polynomials
• Matrix inner product having a matrix symmetric second-order differential operator
• Matrix valued Jacobi polynomials
• Matrix valued orthogonal polynomials of the Jacobi type
• Matrix valued spherical functions associated to the complex projective plane
• Scattering theory and matrix orthogonal polynomials on the real line
• Gaussian quadrature formulae for matrix weights
• A method to find weight matrices having symmetric second-order differential operators with matrix leading coefficient
• Structural formulas for orthogonal matrix polynomials satisfying second-order differential equations. I
• Matrix valued orthogonal polynomials of Jacobi type: the role of group representation theory.
• The algebra of differential operators associated to a family of matrix-valued orthogonal polynomials: Five instructive examples
• Fundamental aspects of the representation theory of Hermitian operators with deficiency index (𝑚,𝑚)
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