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The Riemann-Hilbert problem

Author: D V Anosov; A A Bolibrukh; Matematicheskiĭ institut im. V.A. Steklova.
Publisher: Braunschweig/Wiesbaden : Vieweg, [1994] ©1994
Series: Aspects of mathematics., E ;, volume 22.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book is devoted to Hilbert's 21st problem (the Riemann-Hilbert problem) which belongs to the theory of linear systems of ordinary differential equations in the complex domain. The problem concems the existence of a Fuchsian system with prescribed singularities and monodromy. Hilbert was convinced that such a system always exists. However, this tumed out to be a rare case of a wrong forecast made by hirn. In  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Anosov, D.V.
Riemann-Hilbert problem
(DLC) 95155968
(OCoLC)30566148
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: D V Anosov; A A Bolibrukh; Matematicheskiĭ institut im. V.A. Steklova.
ISBN: 9783322929099 3322929094 9783322929112 3322929116
OCLC Number: 861706079
Notes: "A publication from the Steklov Institute of Mathematics."
Description: 1 online resource (ix, 190 pages).
Contents: 1 Introduction --
2 Counterexample to Hilbert's 21st problem --
3 The Plemelj theorem --
4 Irreducible representations --
5 Miscellaneous topics --
6 The case p = 3 --
7 Fuchsian equations.
Series Title: Aspects of mathematics., E ;, volume 22.
Responsibility: D.V. Anosov, A.A. Bolibruch ; adviser, Armen Sergeev.

Abstract:

This book is devoted to Hilbert's 21st problem (the Riemann-Hilbert problem) which belongs to the theory of linear systems of ordinary differential equations in the complex domain. The problem concems the existence of a Fuchsian system with prescribed singularities and monodromy. Hilbert was convinced that such a system always exists. However, this tumed out to be a rare case of a wrong forecast made by hirn. In 1989 the second author (A.B.) discovered a counterexample, thus 1 obtaining a negative solution to Hilbert's 21st problem. After we recognized that some "data" (singularities and monodromy) can be obtai ned from a Fuchsian system and some others cannot, we are enforced to change our point of view. To make the terminology more precise, we shaII caII the foIIowing problem the Riemann-Hilbert problem for such and such data: does there exist a Fuchsian system having these singularities and monodromy? The contemporary version of the 21 st Hilbert problem is to find conditions implying a positive or negative solution to the Riemann-Hilbert problem.

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