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Field name	Details
Dewey Class	516
Title	The Riemann-Hilbert Problem ([EBook]) : A Publication from the Steklov Institute of Mathematics Adviser: Armen Sergeev / by D. V. Anosov, A. A. Bolibruch.
Author	Anosov, Dmitrij Viktorovic
Added Personal Name	Bolibruch, Andrei Andreevich , 1950-2003
Other name(s)	SpringerLink (Online service)
Publication	Wiesbaden : Vieweg+Teubner Verlag , 1994.
Physical Details	IX, 193 pages, 1 illus. : online resource.
Series	Aspects of mathematics 0179-2156 ; ; 22
ISBN	9783322929099
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-322-92909-9
Links to Related Works	Subject References: Geometry . Mathematics . Authors: Anosov, Dmitrij Viktorovic . author . Bolibruch, Andrei Andreevich 1950-2003 . Corporate Authors: SpringerLink (Online service) . Series: Aspects of mathematics . Classification: 516 .

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The Riemann-Hilbert Problem: A Publication from the Steklov Institute of Mathematics Adviser: Armen Sergeev

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