Please use this identifier to cite or link to this item:
Title: Riemann–Hilbert Problem for the Matrix Laguerre Biorthogonal Polynomials: The Matrix Discrete Painlevé IV
Authors: Branquinho, Amílcar 
Moreno, Ana Foulquié
Fradi, Assil
Mañas, Manuel 
Keywords: discrete integrable systems; matrix biorthogonal polynomials; matrix Pearson equations; non-Abelian discrete Painlevé IV equation; Riemann–Hilbert problems
Issue Date: 2022
Publisher: MDPI
info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB/04106/2020/PT/Center for Research and Development in Mathematics and Applications 
info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP/04106/2020/PT/Center for Research and Development in Mathematics and Applications 
info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UID/MAT/00324/2019/PT/Center for Mathematics, University of Coimbra 
Serial title, monograph or event: Mathematics
Volume: 10
Issue: 8
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. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.
ISSN: 2227-7390
DOI: 10.3390/math10081205
Rights: openAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais
FCTUC Matemática - Artigos em Revistas Internacionais

Files in This Item:
File Description SizeFormat
mathematics-10-01205-v2.pdf383.42 kBAdobe PDFView/Open
Show full item record


checked on Nov 9, 2022

Page view(s)

checked on Mar 27, 2023


checked on Mar 27, 2023

Google ScholarTM




This item is licensed under a Creative Commons License Creative Commons