Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/43945
Title: Orthogonal polynomial interpretation of Δ-Toda equations
Authors: Area, Ivan 
Branquinho, Amílcar 
Foulquié Moreno, Ana 
Godoy, Eduardo 
Issue Date: 2015
Publisher: IOP Publishing
Project: info:eu-repo/grantAgreement/FCT/5876/147205/PT 
Serial title, monograph or event: Journal of Physics A: Mathematical and Theoretical
Volume: 48
Issue: 40
Abstract: In this paper a discretization of Toda equations is analyzed. The correspondence between these Δ-Toda equations for the coefficients of the Jacobi operator and its resolvent function is established. It is shown that the spectral measure of these operators evolve in t like ${(1+x)}^{1-t}\;{\rm{d}}\mu (x)$ where ${\rm{d}}\mu$ is a given positive Borel measure. The Lax pair for the Δ-Toda equations is derived and characterized in terms of linear functionals, where orthogonal polynomials which satisfy an Appell condition with respect to the forward difference operator Δ appear in a natural way. In order to illustrate the results of the paper we work out two examples of Δ-Toda equations related with Jacobi and Laguerre orthogonal polynomials.
URI: http://hdl.handle.net/10316/43945
Other Identifiers: 10.1088/1751-8113/48/40/405206
DOI: 10.1088/1751-8113/48/40/405206
Rights: embargoedAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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