Centre for Mathematics, University of Coimbra

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Type:	Preprint
National /International:	International
Title:	Riemann-Hilbert problem for the matrix Laguerre biorthogonal polynomials: eigenvalue problems and the matrix discrete Painlevé IV
Publication Date:	2019-07-09
Authors:	- Amílcar Branquinho - Ana Foulquié-Moreno - Manuel Mañas
Abstract:	In this paper the Riemann–Hilbert problem, with jump supported on a appropriate curve on the complex plane with a finite end point at the origin, is used for the study of 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. Related matrix eigenvalue problems for second order matrix differential operators and non-Abelian extensions of a family of discrete Painlevé IV equations are discussed.
Institution:	DMUC 19-25
Online version:	http://www.mat.uc.pt...prints/eng_2019.html
Download:	Not available