On the relation between the full Kostant-Toda lattice and multiple orthogonal polynomials

2009/11/15 by D. Barrios Rolanía A. Branquinho A. Foulquié Moreno, Moreno, D. Barrios Rolanía A. Branquinho A. Foulquié
Mathematics · Physics and Astronomy · #15B57 #34K99 #42C05 #47N20 #Classical Analysis and ODEs (math.CA) #Differential Equations and Numerical Methods #FOS: Mathematics #Mathematical functions and polynomials #Nonlinear Waves and Solitons #math.CA #msc:15B57 #msc:34K99 #msc:42C05 #msc:47N20

paper · pdf · doi:10.48550/arxiv.0911.2856

arxiv created 2009/11/15 · openalex publication_date 2009/11/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The correspondence between a high-order non symmetric difference operator with complex coefficients and the evolution of an operator defined by a Lax pair is established. The solution of the discrete dynamical system is studied, giving explicit expressions for the resolvent function and, under some conditions, the representation of the vector of functionals, associated with the solution for our integrable systems. The method of investigation is based on the evolutions of the matrical moments.

Related

• Matrix Orthogonal Polynomial in the theory of Full Kostant-Toda Systems
• Affine Lie algebras, Lax pairs and integrable discrete and continuous systems
• d-orthogonal polynomials, Toda Lattice and Virasoro symmetries
• Determinantal approach to multiple orthogonal polynomials, and the corresponding integrable equations
• Integrable systems on the lattice and orthogonal polynomials of discrete variable