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Dynamics and interpretation of some integrable systems via matrix orthogonal polynomials
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Orientador(es)
Resumo(s)
In this work we characterize a high-order Toda lattice in terms of a family of matrix polynomials orthogonal with respect to a com plex matrix measure. In order to study the solution of this dynamical system, we give explicit expressions for the Weyl function, general ized Markov function, and we also obtain, under some conditions, a representation of the vector of linear functionals associated with this system. We show that the orthogonality is embedded in these
structure and governs the high-order Toda lattice. We also present a Lax-type theorem for the point spectrum of the Jacobi operator
associated with a Toda-type lattice.
Descrição
Palavras-chave
Matrix orthogonal polynomials Linear functional Recurrence relation Operator theory Matrix Sylvester differential equations Toda-type systems Lax-type theorem
Contexto Educativo
Citação
Branquinho, A., Foulquié Moreno, A., & Mendes, A. (2016). Dynamics and interpretation of some integrable systems via matrix orthogonal polynomials. Integral Transforms and Special Functions, 28(1), 74–90. https://doi.org/10.1080/10652469.2016.1250082
Editora
Informa UK Limited
Licença CC
Sem licença CC