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Title: Dynamics and interpretation of some integrable systems via matrix orthogonal polynomials
Author: Branquinho, A.
Moreno, Ana Foulquié
Mendes, A.
Keywords: Matrix orthogonal polynomials
Linear functional
Recurrence relation
Operator theory
Matrix Sylvester differential equations
Issue Date: 2017
Publisher: Taylor & Francis
Abstract: In this work we characterize a high-order Toda lattice in terms of a family of matrix polynomials orthogonal with respect to a complex matrix measure. In order to study the solution of this dynamical system, we give explicit expressions for the Weyl function, generalized 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
Peer review: yes
DOI: 10.1080/10652469.2016.1250082
ISSN: 1065-2469
Appears in Collections:CIDMA - Artigos
CHAG - Artigos

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