Dynamics and interpretation of some integrable systems via matrix orthogonal polynomials

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...

Full description

Saved in:
Bibliographic Details
Published inIntegral transforms and special functions Vol. 28; no. 1; pp. 74 - 90
Main Authors Branquinho, A., Foulquié Moreno, A., Mendes, A.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.01.2017
Taylor & Francis Ltd
Subjects
Lax-type theorem
linear functional
Matrix orthogonal polynomials
matrix Sylvester differential equations
operator theory
Polynomials
recurrence relation
Toda-type systems
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:1065-2469
1476-8291
DOI:10.1080/10652469.2016.1250082