The Riemann-Hilbert Problem

The Riemann-Hilbert Problem
Author :
Publisher : Springer Science & Business Media
Total Pages : 202
Release :
ISBN-10 : 9783322929099
ISBN-13 : 3322929094
Rating : 4/5 (094 Downloads)

Book Synopsis The Riemann-Hilbert Problem by : D. V. Anosov

Download or read book The Riemann-Hilbert Problem written by D. V. Anosov and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


The Riemann-Hilbert Problem Related Books

The Riemann-Hilbert Problem
Language: en
Pages: 202
Authors: D. V. Anosov
Categories: Mathematics
Type: BOOK - Published: 2013-06-29 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

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
Riemann-Hilbert Problems, Their Numerical Solution, and the Computation of Nonlinear Special Functions
Language: en
Pages: 370
Authors: Thomas Trogdon
Categories: Mathematics
Type: BOOK - Published: 2015-12-22 - Publisher: SIAM

DOWNLOAD EBOOK

Riemann?Hilbert problems are fundamental objects of study within complex analysis. Many problems in differential equations and integrable systems, probability a
Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach
Language: en
Pages: 273
Authors: Percy Deift
Categories: Mathematics
Type: BOOK - Published: 2000 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

This volume expands on a set of lectures held at the Courant Institute on Riemann-Hilbert problems, orthogonal polynomials, and random matrix theory. The goal o
Painlevé Transcendents
Language: en
Pages: 570
Authors: Athanassios S. Fokas
Categories: Mathematics
Type: BOOK - Published: 2023-11-20 - Publisher: American Mathematical Society

DOWNLOAD EBOOK

At the turn of the twentieth century, the French mathematician Paul Painlevé and his students classified second order nonlinear ordinary differential equations