Matrix orthogonal Laurent polynomials on the unit circle and Toda type integrable systems

DOI10.1016/j.aim.2014.06.019zbMath1305.33018arXiv1312.0150OpenAlexW1995838060MaRDI QIDQ400990

Gerardo Ariznabarreta, Manuel Mañas

Publication date: 26 August 2014

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

Full work available at URL: https://arxiv.org/abs/1312.0150

zbMATH Keywords

Borel-Gauss factorizationChristoffel-Darboux kernelsmatrix orthogonal Laurent polynomialsToda type integrable hierarchies

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Noncommutative dynamical systems (46L55) Lattice dynamics and infinite-dimensional dissipative dynamical systems (37L60)

Related Items (19)

Multivariate orthogonal Laurent polynomials and integrable systems ⋮ A generalization of Laurent biorthogonal polynomials and related integrable lattices ⋮ Multivariate Toda hierarchies and biorthogonal polynomials ⋮ Multivariate orthogonal polynomials and integrable systems ⋮ The Toda and Painlevé systems associated with semiclassical matrix-valued orthogonal polynomials of Laguerre type ⋮ Revisiting biorthogonal polynomials: an \(LU\) factorization discussion ⋮ CMV block matrices for symmetric matrix measures on the unit circle ⋮ Pearson equations for discrete orthogonal polynomials: I. Generalized hypergeometric functions and Toda equations ⋮ Laguerre–Freud equations for three families of hypergeometric discrete orthogonal polynomials ⋮ Matrix-valued Gegenbauer-type polynomials ⋮ Duality and difference operators for matrix valued discrete polynomials on the nonnegative integers ⋮ On the Hahn's property for matrix orthogonal polynomials on the unit circle ⋮ Non-Abelian Toda-type equations and matrix valued orthogonal polynomials ⋮ Matrix Uvarov transformation on the unit circle: asymptotic properties ⋮ Christoffel transformation for a matrix of bi-variate measures ⋮ On a Christoffel transformation for matrix measures supported on the unit circle ⋮ Matrix-valued Laurent polynomials, parametric linear systems and integrable systems ⋮ Pearson equations for discrete orthogonal polynomials. III: Christoffel and Geronimus transformations ⋮ Matrix biorthogonal polynomials on the real line: Geronimus transformations

Uses Software

• OPQ

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