Detalhes bibliográficos
| Resumo: | 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. |
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| Autores principais: | Area, I. |
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| Outros Autores: | Branquinho, A.; Moreno, A. Foulquié; Godoy, E. |
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| Assunto: | Orthogonal polynomials Difference operators Operator theory Toda lattices |
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| Ano: | 2016 |
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| País: | Portugal |
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| Tipo de documento: | artigo |
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| Tipo de acesso: | acesso aberto |
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| Instituição associada: | Universidade de Aveiro |
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| Idioma: | inglês |
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| Origem: | RIA - Repositório Institucional da Universidade de Aveiro |
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