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https://hdl.handle.net/10316/43839
Title: | Characterizations of Δ-Volterra lattice: A symmetric orthogonal polynomials interpretation | Authors: | Area, I. Branquinho, Amílcar Foulquié Moreno, A. Godoy, E. |
Issue Date: | 2016 | Publisher: | Elsevier | Project: | info:eu-repo/grantAgreement/FCT/5876/147206/PT | Serial title, monograph or event: | Journal of Mathematical Analysis and Applications | Volume: | 433 | Issue: | 1 | Abstract: | In this paper we introduce the Δ-Volterra lattice which is interpreted in terms of symmetric orthogonal polynomials. It is shown that the measure of orthogonality associated with these systems of orthogonal polynomials evolves in t like (1+x^2)^1−t μ(x) where μ is a given positive Borel measure. Moreover, the Δ-Volterra lattice is related to the Δ-Toda lattice from Miura or Bäcklund transformations. The main ingredients are orthogonal polynomials which satisfy an Appell condition with respect to the forward difference operator Δ and the characterization of the point spectrum of a Jacobian operator that satisfies a Δ-Volterra equation (Lax type theorem). We also provide an explicit example of solutions of Δ-Volterra and Δ-Toda lattices, and connect this example with the results presented in the paper. | URI: | https://hdl.handle.net/10316/43839 | DOI: | 10.1016/j.jmaa.2015.07.051 10.1016/j.jmaa.2015.07.051 |
Rights: | embargoedAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
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