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Title: Riemann–Hilbert problem for the matrix Laguerre biorthogonal polynomials: the matrix discrete Painlevé IV
Author: Branquinho, Amílcar
Moreno, Ana Foulquié
Fradi, Assil
Mañas, Manuel
Keywords: Riemann–Hilbert problems
Matrix Pearson equations
Matrix biorthogonal polynomials
Discrete integrable systems
Non-Abelian discrete Painlevé IV equation
Issue Date: 7-Apr-2022
Publisher: MDPI
Abstract: In this paper, the Riemann–Hilbert problem, with a jump supported on an appropriate curve on the complex plane with a finite endpoint at the origin, is used for the study of the corresponding matrix biorthogonal polynomials associated with Laguerre type matrices of weights—which are constructed in terms of a given matrix Pearson equation. First and second order differential systems for the fundamental matrix, solution of the mentioned Riemann–Hilbert problem, are derived. An explicit and general example is presented to illustrate the theoretical results of the work. The non-Abelian extensions of a family of discrete Painlevé IV equations are discussed.
Peer review: yes
DOI: 10.3390/math10081205
ISSN: 2227-7390
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Appears in Collections:CIDMA - Artigos
CHAG - Artigos

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