On sufficient conditions for the positive solvability of the Riemann- Hilbert problem
type: Item
instance of: scholarly article
title: On sufficient conditions for the positive solvability of the Riemann- Hilbert problem
zbMATH Open document ID: 0790.34001
DOI: 10.1007/BF02102113
author: A. A. Bolibrukh
published in: Mathematical Notes
publication date: 1994-02-08T00:00:00Z
review text: In a previous paper the author showed that the 21-st Hilbert problem has no solution in a general case. But it is known [see the author, Usp. Mat. Nauk 45, No. 2, 3-47 (1990; Zbl 0706.34005); \textit{V. P. Kostov}, C.R. Acad. Sci., Paris, Ser. I 315, No. 2, 143-148 (1992; Zbl 0772.34007)]that the problem has a solution in the following cases: if a monodromy group lies in GL(2); if a monodromy group is irreducible. A natural question arises in this regard: How can one characterize all monodromy groups such that the Riemann-Hilbert problem is solvable in a positive sense? In the present paper the author has shown that if one can admit the existence of at most one irregular singular point then the problem has a solution. He also indicates new classes of monodromy groups such that the Riemann-Hilbert problem has a positive solution.
Mathematics Subject Classification ID: 34M99
Mathematics Subject Classification ID: 12H05
zbMATH DE Number: 484233
zbMATH Keywords: 21-st Hilbert problem
zbMATH Keywords: monodromy group
zbMATH Keywords: Riemann-Hilbert problem
zbMATH Keywords: irregular singular point
reviewed by: Mykola Grygorenko
MaRDI profile type: Publication
cites work: Q4205673
cites work: The Riemann-Hilbert problem
cites work: Q3964699
cites work: Q3987224
cites work: Q3202403
cites work: Q5737197
cites work: Q5328253
cites work: Q4276011
description: scientific article; zbMATH DE number 484233