A noncommutative version of the bispectral problem.

DOI10.1016/S0377-0427(03)00548-XzbMath1038.39012MaRDI QIDQ1412819

Plamen Iliev, F. Alberto Gruenbaum

Publication date: 25 November 2003

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

zbMATH Keywords

difference operatorsToda latticematrix-valued functionsbispectral problem

Mathematics Subject Classification ID

Difference operators (39A70) Linear difference operators (47B39)

Related Items

Matrix bispectrality of full rank one algebras ⋮ The Darboux process and a noncommutative bispectral problem: some explorations and challenges ⋮ Noncommutative bispectral Darboux transformations ⋮ Matrix bispectrality and noncommutative algebras: beyond the prolate spheroidals ⋮ Matrix valued Jacobi polynomials ⋮ Matrix valued orthogonal polynomials of the Jacobi type ⋮ A survey on orthogonal matrix polynomials satisfying second order differential equations ⋮ Spin Calogero particles and bispectral solutions of the matrix KP hierarchy ⋮ Matrix polynomials satisfying first order differential equations and three term recurrence relations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Differential equations in the spectral parameter
• Differential equations in the spectral parameter for matrix differential operators
• Collisions of Calogero-Moser particles and an adelic Grassmannian (with an appendix by I. G. Macdonald)
• On a class of polynomials connected with the Korteweg-de Vries equation
• The spectrum of difference operators and algebraic curves
• Rational solutions of nonlinear evolution equations, vertex operators, and bispectrality
• Solving second-order matrix differential equations with regular singular points avoiding the increase of the problem dimension
• Bispectral algebras of commuting ordinary differential operators
• The quantum dynamics of the compactified trigonometric Ruijsenaars-Schneider model
• Laguerre matrix polynomials and systems of second-order differential equations
• Matrix inner product having a matrix symmetric second-order differential operator
• \(\mathcal{D}\)-modules and Darboux transformations
• Matrix valued Jacobi polynomials
• Associated polynomials, spectral matrices and the bispectral problem
• Differential equations compatible with KZ equations
• Matrix valued spherical functions associated to the complex projective plane
• Mutual integrability, quadratic algebras, and dynamical symmetry
• Multidimensional Baker-Akhiezer functions and Huygens' principle
• Darboux transformations of bispectral quantum integrable systems
• Certain differential equations for Tchebycheff polynomials
• A rational analogue of the Krall polynomials
• A matrix-valued solution to Bochner's problem
• Bispectral commutative ordinary differential operators.
• Rational and elliptic solutions of the korteweg-de vries equation and a related many-body problem
• NonAbelian nonlinear lattice equations on finite interval
• Bispectral rings of difference operators
• MATRIX VALUED SPHERICAL FUNCTIONS ASSOCIATED TO THE THREE DIMENSIONAL HYPERBOLIC SPACE
• Huygens' principle and integrability
• Formulas for \(q\)-spherical functions using inverse scattering theory of reflectionless Jacobi operators