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The Riemann-Hilbert Problem

A Publication from the Steklov Institute of Mathematics Adviser: Armen Sergeev

  • Book
  • © 1994

Overview

Authors:
  1. D. V. Anosov

    1. Steklov Institute of Mathematics, Moscow/CIS, Russia

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  2. A. A. Bolibruch

    1. Steklov Institute of Mathematics, Moscow/CIS, Russia

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Aspects of Mathematics (ASMA, volume 22)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-IX
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  2. Introduction

    • D. V. Anosov, A. A. Bolibruch
    Pages 1-13

  3. Counterexample to Hilbert’s 21st problem

    • D. V. Anosov, A. A. Bolibruch
    Pages 14-50

  4. The Plemelj theorem

    • D. V. Anosov, A. A. Bolibruch
    Pages 51-76

  5. Irreducible representations

    • D. V. Anosov, A. A. Bolibruch
    Pages 77-88

  6. Miscellaneous topics

    • D. V. Anosov, A. A. Bolibruch
    Pages 89-132

  7. The case p = 3

    • D. V. Anosov, A. A. Bolibruch
    Pages 133-157

  8. Fuchsian equations

    • D. V. Anosov, A. A. Bolibruch
    Pages 158-184

  9. Back Matter

    Pages 185-193
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Keywords

About this book

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.

Authors and Affiliations

  • Steklov Institute of Mathematics, Moscow/CIS, Russia

    D. V. Anosov, A. A. Bolibruch

About the authors

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

Bibliographic Information

  • Book Title: The Riemann-Hilbert Problem

  • Book Subtitle: A Publication from the Steklov Institute of Mathematics Adviser: Armen Sergeev

  • Authors: D. V. Anosov, A. A. Bolibruch

  • Series Title: Aspects of Mathematics

  • DOI: https://doi.org/10.1007/978-3-322-92909-9

  • Publisher: Vieweg+Teubner Verlag Wiesbaden

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Fachmedien Wiesbaden 1994

  • Softcover ISBN: 978-3-322-92911-2Published: 23 August 2014

  • eBook ISBN: 978-3-322-92909-9Published: 29 June 2013

  • Series ISSN: 0179-2156

  • Edition Number: 1

  • Number of Pages: IX, 193

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Geometry

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