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Uspekhi Mat. Nauk, 2011, Volume 66, Issue 1(397), Pages 37–64 (Mi umn9405)  

Riemann–Hilbert problem for scalar Fuchsian equations and related problems

I. V. Vyugin

A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: This paper is devoted to the Riemann–Hilbert problem for scalar Fuchsian equations: the problem of constructing a scalar Fuchsian equation from a representation of the monodromy and a family of singular points. The results of Bolibrukh [5], van der Put and Singer [7], and the author [10], generalized to a unified theorem provided with a new proof, form the main part of the paper. Some possible applications of these results are also discussed.
Bibliography: 16 titles.

Keywords: Fuchsian equations and systems, Riemann–Hilbert problem, monodromy, bundle, connection.

DOI: https://doi.org/10.4213/rm9405

Full text: PDF file (668 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2011, 66:1, 35–62

Bibliographic databases:

Document Type: Article
UDC: 517.927.7
MSC: Primary 35Q15; Secondary 30E25, 31A25, 31B20, 34M50
Received: 08.12.2010

Citation: I. V. Vyugin, “Riemann–Hilbert problem for scalar Fuchsian equations and related problems”, Uspekhi Mat. Nauk, 66:1(397) (2011), 37–64; Russian Math. Surveys, 66:1 (2011), 35–62

Citation in format AMSBIB
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