The Darboux process and a noncommutative bispectral problem: some explorations and challenges

DOI10.1007/978-0-8176-8244-6_6zbMath1263.34022OpenAlexW142694538MaRDI QIDQ2914653

F. Alberto Gruenbaum

Publication date: 20 September 2012

Published in: Progress in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-0-8176-8244-6_6

zbMATH Keywords

Darboux processmatrix-valued orthogonal polynomials

Mathematics Subject Classification ID

Inverse problems involving ordinary differential equations (34A55) Ordinary differential operators (34L99) Research exposition (monographs, survey articles) pertaining to ordinary differential equations (34-02)

Related Items (13)

Darboux transformations for CMV matrices ⋮ Stochastic LU factorizations, Darboux transformations and urn models ⋮ An extension of the Geronimus transformation for orthogonal matrix polynomials on the real line ⋮ Darboux transformations for orthogonal polynomials on the real line and on the unit circle ⋮ Non-Abelian integrable hierarchies: matrix biorthogonal polynomials and perturbations ⋮ The Darboux process and time-and-band limiting for matrix orthogonal polynomials ⋮ The bilateral birth–death chain generated by the associated Jacobi polynomials ⋮ Matrix-valued Gegenbauer-type polynomials ⋮ The spectral matrices associated with the stochastic Darboux transformations of random walks on the integers ⋮ Elementary examples of solutions to Bochner's problem for matrix differential operators ⋮ Christoffel transformation for a matrix of bi-variate measures ⋮ Stochastic Darboux transformations for quasi-birth-and-death processes and urn models ⋮ Spectral theory of multiple intervals

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