Linear Differential Equations in the Complex Domain : Problems of Analytic Continuation

by Sibuya, Yasutaka

• ISBN13: 9780821846766
• ISBN10: 0821846760
• Format: Paperback
• Copyright: 2008-08-01
• Publisher: Amer Mathematical Society

Summary

"This book is a translation of a 1976 book originally written in Japanese. The main attention is paid to intrinsic aspects of problems related to linear ordinary differential equations in complex domains. Examples of the problems discussed in the book include the Riemann problem on the Riemann sphere, a characterization of regular singularities, and a classification of meromorphic differential equations." "This book introduces the reader to the essential facts concerning the structure of solutions of linear differential equations in the complex domain and illuminates the intrinsic meaning of older results by means of more modern ideas. A useful reference for research mathematicians, this book would also be suitable as a textbook in a graduate course or seminar."--BOOK JACKET.

Table of Contents

Structures of Analytic Continuation	p. 1
Existence Theorem of Grauert	p. 31
A Theorem of G. D. Birkhoff	p. 69
The Riemann Problem	p. 95
Linear Differential Equations on a Sectorial Domain	p. 115
The Stokes Phenomena	p. 143
The Hukuhara-Turrittin Theorem in Terms of D[actual symbol not reproducible]-Modules	p. 177
Gevrey Asymptotics	p. 189
Cohomological Methods	p. 215
k-Summability	p. 229
Differential Equations Containing Parameters	p. 241
References	p. 257
Index	p. 265
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