Matrix biorthogonal polynomials: eigenvalue problems and non-Abelian discrete Painlevé equations. A Riemann-Hilbert problem perspective

DOI10.1016/j.jmaa.2020.124605zbMath1458.37073arXiv1807.07119OpenAlexW3087431591MaRDI QIDQ2227574

Manuel Mañas, Amílcar Branquinho, Ana Foulquié Moreno

Publication date: 15 February 2021

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.07119

zbMATH Keywords

Markov functionsRiemann-Hilbert problemsdiscrete integrable systemsmatrix Pearson equationsmatrix biorthogonal polynomialsnonabelian discrete Painlevé I equation

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Other special orthogonal polynomials and functions (33C47) Lattice dynamics; integrable lattice equations (37K60) Painlevé-type functions (33E17) Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain (34M50) Matrix exponential and similar functions of matrices (15A16) Integrable difference and lattice equations; integrability tests (39A36) Nonautonomous Hamiltonian dynamical systems (Painlevé equations, etc.) (37J65) Completely integrable discrete dynamical systems (37J70)

Related Items

Two variable Freud orthogonal polynomials and matrix Painlevé-type difference equations ⋮ Multivariate Toda hierarchies and biorthogonal polynomials ⋮ On matrix Painlevé-4 equations ⋮ Riemann-Hilbert problem and matrix biorthogonal polynomials ⋮ Asymptotics of matrix valued orthogonal polynomials on \([-1, 1\)] ⋮ Matrix Jacobi biorthogonal polynomials via Riemann–Hilbert problem ⋮ Jacobi-Piñeiro Markov chains ⋮ Hahn multiple orthogonal polynomials of type I: hypergeometric expressions ⋮ Non-Abelian Toda-type equations and matrix valued orthogonal polynomials ⋮ Pearson equations for discrete orthogonal polynomials. III: Christoffel and Geronimus transformations ⋮ Multiple orthogonal polynomials: Pearson equations and Christoffel formulas

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