Publication: Riemann-Hilbert problem for the matrix Laguerre biorthogonal polynomials: the matrix discrete Painleve IV
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2022-04-07
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MDPI
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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 Painleve IV equations are discussed.
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© 2022 by the authors.
A.B. acknowledges Centro de Matematica da Universidade de Coimbra (CMUC)-UID/MAT/00324/2019, funded by the Portuguese Government through FCT/MEC and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020. A.F.M. and A.F. acknowledges CIDMA Center for Research and Development in Mathematics and Applications (University of Aveiro) and the Portuguese Foundation for Science and Technology (FCT) within project UIDB/04106/2020 and UIDP/04106/2020. M.M. thanks financial support from the Spanish "Agencia Estatal de Investigacion" research project [PGC2018-096504-B-C33], Ortogonalidad y Aproximacioon: Teoria y Aplicaciones en FisicaMatematica.