The Riemann-Hilbert Problem: A Publication from the Steklov Institute of Mathematics Adviser: Armen Sergeev
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Wiesbaden
Vieweg+Teubner Verlag
1994
|
| Schriftenreihe: | Aspects of Mathematics
22 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (IX, 193 p) |
| ISBN: | 9783322929099 9783322929112 |
| ISSN: | 0179-2156 |
| DOI: | 10.1007/978-3-322-92909-9 |
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| 500 | |a 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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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:11Z |
| institution | BVB |
| isbn | 9783322929099 9783322929112 |
| issn | 0179-2156 |
| language | English |
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| spelling | Anosov, D. V. Verfasser aut The Riemann-Hilbert Problem A Publication from the Steklov Institute of Mathematics Adviser: Armen Sergeev by D. V. Anosov, A. A. Bolibruch Wiesbaden Vieweg+Teubner Verlag 1994 1 Online-Ressource (IX, 193 p) txt rdacontent c rdamedia cr rdacarrier Aspects of Mathematics 22 0179-2156 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 Mathematics Geometry Mathematik Bolibruch, A. A. Sonstige oth https://doi.org/10.1007/978-3-322-92909-9 Verlag Volltext |
| spellingShingle | Anosov, D. V. The Riemann-Hilbert Problem A Publication from the Steklov Institute of Mathematics Adviser: Armen Sergeev Mathematics Geometry Mathematik |
| title | The Riemann-Hilbert Problem A Publication from the Steklov Institute of Mathematics Adviser: Armen Sergeev |
| title_auth | The Riemann-Hilbert Problem A Publication from the Steklov Institute of Mathematics Adviser: Armen Sergeev |
| title_exact_search | The Riemann-Hilbert Problem A Publication from the Steklov Institute of Mathematics Adviser: Armen Sergeev |
| title_full | The Riemann-Hilbert Problem A Publication from the Steklov Institute of Mathematics Adviser: Armen Sergeev by D. V. Anosov, A. A. Bolibruch |
| title_fullStr | The Riemann-Hilbert Problem A Publication from the Steklov Institute of Mathematics Adviser: Armen Sergeev by D. V. Anosov, A. A. Bolibruch |
| title_full_unstemmed | The Riemann-Hilbert Problem A Publication from the Steklov Institute of Mathematics Adviser: Armen Sergeev by D. V. Anosov, A. A. Bolibruch |
| title_short | The Riemann-Hilbert Problem |
| title_sort | the riemann hilbert problem a publication from the steklov institute of mathematics adviser armen sergeev |
| title_sub | A Publication from the Steklov Institute of Mathematics Adviser: Armen Sergeev |
| topic | Mathematics Geometry Mathematik |
| topic_facet | Mathematics Geometry Mathematik |
| url | https://doi.org/10.1007/978-3-322-92909-9 |
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