Estudo Geralhttps://estudogeral.sib.uc.ptThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Tue, 22 Sep 2020 14:33:47 GMT2020-09-22T14:33:47Z5051Dynamics and interpretation of some integrable systems via matrix orthogonal polynomialshttp://hdl.handle.net/10316/43942Title: Dynamics and interpretation of some integrable systems via matrix orthogonal polynomials
Authors: Branquinho, Amílcar; Foulquié Moreno, Ana; Mendes, Ana
Abstract: n 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.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10316/439422016-01-01T00:00:00ZOn the full Kostant–Toda system and the discrete Korteweg–de Vries equationshttp://hdl.handle.net/10316/43845Title: On the full Kostant–Toda system and the discrete Korteweg–de Vries equations
Authors: Barrios Rolanía, Dolores; Branquinho, Amílcar; Foulquié Moreno, Ana
Abstract: The relation between the solutions of the full Kostant–Toda lattice and the discrete Korteweg–de Vries equation is analyzed. A method for constructing solutions of these systems is given. As a consequence of the matricial interpretation of this method, the transform of Darboux is extended for general Hessenberg banded matrices.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10316/438452013-01-01T00:00:00ZOrthogonal polynomial interpretation of Δ-Toda equationshttp://hdl.handle.net/10316/43945Title: Orthogonal polynomial interpretation of Δ-Toda equations
Authors: Area, Ivan; Branquinho, Amílcar; Foulquié Moreno, Ana; Godoy, Eduardo
Abstract: In this paper a discretization of Toda equations is analyzed. The correspondence between these Δ-Toda equations for the coefficients of the Jacobi operator and its resolvent function is established. It is shown that the spectral measure of these operators evolve in t like ${(1+x)}^{1-t}\;{\rm{d}}\mu (x)$ where ${\rm{d}}\mu$ is a given positive Borel measure. The Lax pair for the Δ-Toda equations is derived and characterized in terms of linear functionals, where orthogonal polynomials which satisfy an Appell condition with respect to the forward difference operator Δ appear in a natural way. In order to illustrate the results of the paper we work out two examples of Δ-Toda equations related with Jacobi and Laguerre orthogonal polynomials.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10316/439452015-01-01T00:00:00ZSecond-order differential equations in the Laguerre–Hahn classhttp://hdl.handle.net/10316/43841Title: Second-order differential equations in the Laguerre–Hahn class
Authors: Branquinho, Amílcar; Foulquié Moreno, Ana; Paiva, Anabela; Rebocho, Maria das Neves
Abstract: Laguerre–Hahn families on the real line are characterized in terms of second-order differential equations with matrix coefficients for vectors involving the orthogonal polynomials and their associated polynomials, as well as in terms of second-order differential equation for the functions of the second kind. Some characterizations of the classical families are derived.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10316/438412015-01-01T00:00:00ZAn extension of Markov’s Theoremhttp://hdl.handle.net/10316/44496Title: An extension of Markov’s Theorem
Authors: Branquinho, Amílcar; Fidalgo Prieto, Ulises; Foulquié Moreno, Ana
Abstract: We give a general sufficient condition for the uniform convergence of sequences of type II Hermite-Padé approximants associated with Nikishin systems of functions.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10316/444962014-01-01T00:00:00Z