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Riemann--Hilbert problems, matrix orthogonal polynomials and discrete matrix equations with singularity confinement.

Чт, 06/02/2011 - 15:01 — SomNambul
Authors: Giovanni A. Cassatella-Contra, Manuel Manas
Subjects: Classical Analysis and ODEs
link: http://arxiv.org/abs/1106.0036
Abstract

In this paper matrix orthogonal polynomials in the real line are described in
terms of a Riemann--Hilbert problem. This approach provides an easy derivation
of discrete equations for the corresponding matrix recursion coefficients. The
discrete equation is explicitly derived in the matrix Freud case, associated
with matrix quartic potentials. It is shown that, when the initial condition
and the measure are simultaneously triangularizable, this matrix discrete
equation possesses the singularity confinement property, independently if the
solution under consideration is given by recursion coefficients to quartic
Freud matrix orthogonal polynomials or not.

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