Painlevé equations and orthogonal polynomials on the unit circle
Orthogonal polynomials on the unit circle and related studies
Ortogonal polynomials on the real line and on the unit circle
| Full text | |
| Author(s): |
Bracciali, Cleonice F.
;
Perez, Teresa E.
Total Authors: 2
|
| Document type: | Journal article |
| Source: | Applied Mathematics and Computation; v. 309, p. 142-155, SEP 15 2017. |
| Web of Science Citations: | 1 |
| Abstract | |
We explore the connection between an infinite system of particles in R-2 described by a bi-dimensional version of the Toda equations with the theory of orthogonal polynomials in two variables. We define a 2D Toda lattice in the sense that we consider only one time variable and two space variables describing a mesh of interacting particles over the plane. We show that this 2D Toda lattice is related with the matrix coefficients of the three term relations of bivariate orthogonal polynomials associated with an exponential modification of a positive measure. Moreover, block Lax pairs for 2D Toda lattices are deduced. (C) 2017 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 14/22571-2 - Orthogonal and Similar Polynomials with some analytical and numerical applications |
| Grantee: | Cleonice Fátima Bracciali |
| Support Opportunities: | Regular Research Grants |