The Riemann-Hilbert Problem : A Publication from the Steklov Institute of Mathematics Adviser: Armen Sergeev PDF
by D. V. Anosov, A. A. Bolibruch
Part of the Aspects of Mathematics series
Description
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.
Information
-
Download - Immediately Available
- Format:PDF
- Publisher:Vieweg+Teubner Verlag
- Publication Date:29/06/2013
- Category:
- ISBN:9783322929099
Information
-
Download - Immediately Available
- Format:PDF
- Publisher:Vieweg+Teubner Verlag
- Publication Date:29/06/2013
- Category:
- ISBN:9783322929099
