Padé approximants and complex high order Toda lattices

DOI10.1016/S0377-0427(02)00866-XzbMath1031.42026OpenAlexW2032644129MaRDI QIDQ1811586

Alexander I. Aptekarev, Amílcar Branquinho

Publication date: 17 June 2003

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

Full work available at URL: https://doi.org/10.1016/s0377-0427(02)00866-x

zbMATH Keywords

orthogonal polynomialsToda latticethree-term recurrence relationsdirect and inverse spectral problemisospectral deformation of Jacobi matrixtransformations of the measure

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) 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) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Continued fractions; complex-analytic aspects (30B70) Lattice dynamics; integrable lattice equations (37K60)

Related Items (8)

Multidimensional Toda lattices: continuous and discrete time ⋮ Solution of the finite Toda lattice with self-consistent source ⋮ Orthogonal polynomial interpretation of \(q\)-Toda and \(q\)-Volterra equations ⋮ Dynamics and interpretation of some integrable systems via matrix orthogonal polynomials ⋮ Characterizations of \(\Delta\)-Volterra lattice: a symmetric orthogonal polynomials interpretation ⋮ Matrix Toda and Volterra lattices ⋮ Dynamics and interpretation of some integrable systems via multiple orthogonal polynomials ⋮ Spectrum and generation of solutions of the Toda lattice

Cites Work

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• Toda-type differential equations for the recurrence coefficients of orthogonal polynomials and Freud transformation
• Three integrable Hamiltonian systems connected with isospectral deformations
• On an explicitly soluble system of nonlinear differential equations related to certain Toda lattices
• Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials
• ON UNIFORM CONVERGENCE OF DIAGONAL PADÉ APPROXIMANTS
• Criterion for the Resolvent Set of Nonsymmetric Tridiagonal Operators
• CONVEX DOMAINS WITH NONCOMPACT AUTOMORPHISM GROUPS

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