Orthogonal polynomial interpretation of q-Toda and q-Volterra equations

The correspondences between dynamics of q-Toda and q-Volterra equations for the coefficients of the Jacobi operator and its resolvent function are established. The orthogonal polynomials associated with these Jacobi operators satisfy an Appell condition, with respect to the q-difference operator Dq...

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Bibliographic Details
Main Author: Área, Ivan (author)
Other Authors: Branquinho, Amílcar (author), Godoy, Eduardo (author), Moreno, Ana Foulquié (author)
Format: article
Language:eng
Published: 2018
Subjects:
q-Difference equations
Recurrence relations
Orthogonal polynomials
q-Toda equations
q-Volterra equations
Lax type theorems
Online Access:http://hdl.handle.net/10773/21862
Country:Portugal
Oai:oai:ria.ua.pt:10773/21862
Description
Summary:The correspondences between dynamics of q-Toda and q-Volterra equations for the coefficients of the Jacobi operator and its resolvent function are established. The orthogonal polynomials associated with these Jacobi operators satisfy an Appell condition, with respect to the q-difference operator Dq . Lax type theorems for the point spectrum of the Jacobi operators associated with these equations are obtained. Examples related with the big q-Legendre, discrete q-Hermite I, and little q-Laguerre orthogonal polynomials and q-Toda and q-Volterra equations are given.

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