The Riemann-Hilbert Problem

Der Band befaßt sich mit Differentialgleichungen vom Fuchsschen Typ und löst ein Problem, das von Hilbert 1900 gestellt wurde.

Autorentext

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

Klappentext

The Riemann-Hilbert problem (Hilbert's 21st problem) belongs to the theory of linear systems of ordinary differential equations in the complex domain. The problem concerns the existence of a Fuchsian system with prescribed singularities and monodromy. Hilbert was convinced that such a system always exists. However, this turned out to be a rare case of a wrong forecast made by him. In 1989 the second author (A. B.) discovered a counterexample, thus obtaining a negative solution to Hilbert's 21st problem in its original form.

Inhalt
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.