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Title: Characterizations of Δ-Volterra lattice: a symmetric orthogonal polynomials interpretation
Author: Area, I.
Branquinho, A.
Moreno, A. Foulquié
Godoy, E.
Keywords: Orthogonal polynomials
Difference operators
Operator theory
Toda lattices
Issue Date: 1-Jan-2016
Publisher: Elsevier
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+x2)1−tμ(x)(1+x2)1−tμ(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.
Peer review: yes
DOI: 10.1016/j.jmaa.2015.07.051
ISSN: 0022-247X
Appears in Collections:CIDMA - Artigos
CHAG - Artigos

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