Matrix polynomials satisfying first order differential equations and three term recurrence relations

DOI10.1016/j.cam.2009.02.064zbMath1179.15014OpenAlexW2014786518MaRDI QIDQ1044642

Mirta Castro Smirnova

Publication date: 18 December 2009

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2009.02.064

zbMATH Keywords

difference equationsthree term recurrence relationcommutatormatrix orthogonalityfirst order differential equationBochner problemnoncommutative bispectral problemmatrix valued polynomials

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Linear ordinary differential equations and systems (34A30) Additive difference equations (39A10) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

Cites Work

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• Differential equations in the spectral parameter
• The noncommutative bispectral problem for operators of order one
• Matrix inner product having a matrix symmetric second-order differential operator
• A noncommutative version of the bispectral problem.
• A survey on orthogonal matrix polynomials satisfying second order differential equations
• The algebra of differential operators associated to a weight matrix
• Some examples of orthogonal matrix polynomials satisfying odd order differential equations
• Orthogonal matrix polynomials satisfying first order differential equations: a collection of instructive examples
• 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)
• Matrix-valued orthogonal polynomials on the real line: some extensions of the classical theory

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