The noncommutative bispectral problem for operators of order one

DOI10.1007/S00365-007-0676-YzbMath1157.39001OpenAlexW2022909255MaRDI QIDQ937241

F. Alberto Gruenbaum, Mirta Castro Smirnova

Publication date: 20 August 2008

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00365-007-0676-y

zbMATH Keywords

matrix valued orthogonal polynomialsad-conditionsBochner problemfirst order recurrence relationnatrix valued polynomialsnoncommutative bispectral problem

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Matrix equations and identities (15A24) Additive difference equations (39A10) Rings of differential operators (associative algebraic aspects) (16S32) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

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The Darboux process and time-and-band limiting for matrix orthogonal polynomials ⋮ Matrix differential equations and scalar polynomials satisfying higher order recursions ⋮ Matrix polynomials satisfying first order differential equations and three term recurrence relations

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