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https://hdl.handle.net/10316/43945
Title: | Orthogonal polynomial interpretation of Δ-Toda equations | Authors: | Area, Iván 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: | https://hdl.handle.net/10316/43945 | DOI: | 10.1088/1751-8113/48/40/405206 10.1088/1751-8113/48/40/405206 |
Rights: | embargoedAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
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