Please use this identifier to cite or link to this item: http://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: http://hdl.handle.net/10316/43839
Other Identifiers: 10.1016/j.jmaa.2015.07.051
DOI: 10.1016/j.jmaa.2015.07.051
Rights: embargoedAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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