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

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.

List of 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.

About the author

Prof. Anosov und Prof. Bolibrukh sind beide am Steklov Institut in Moskau tätig.

Product details

• Authors: D Anosov, D V Anosov, D. V. Anosov, A A Bolibruch, A. A. Bolibruch
• Publisher: Vieweg+Teubner
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2014
• EAN: 9783322929112
• ISBN: 978-3-32-292911-2
• No. of pages: 193
• Dimensions: 211 mm x 12 mm x 297 mm
• Weight: 575 g
• Illustrations: IX, 193 p. 1 illus.
• Series: Aspects of Mathematics; Aspects of Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Geometry; Riemannsche Geometrie, Differenzialgeometrie / Riemann, MATHEMATICS / Geometry / General, Monodromy; differential equation; eXist; equation; form; ordinary differential equation; presentation; system