Asymptotic Analysis for Integrable Connections with Irregular Singular Points
- PDF / 7,496,757 Bytes
- 169 Pages / 468 x 684 pts Page_size
- 43 Downloads / 208 Views
1075
Hideyuki Majima
Asymptotic Analysis for Integrable Connections with Irregular Singular Points
Springer-Verlag Berlin Heidelberg New York Tokyo 1984
Author
Hideyuki Majima Department of Mathematics, Faculty of Science, University of Tokyo Hongo, Tokyo 113, Japan
AMS Subject Classification (1980): 58A 17, 35C20; 32L10 ISBN 3-540-13375-5 Springer-Verlag Berlin Heidelberg New York Tokyo ISBN 0-387-13375-5 Springer-Verlag New York Heidelberg Berlin Tokyo
This work is subjectto copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich.
© by Springer-Verlag Berlin Heidelberg 1984 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach / Bergstr. 2146/3140-543210
Dedicated to the Author's Grand-Professor Masuo Hukuhara on his 77th Birthday
Abstract Using strongly asymptotic expansions of functions of several variables, we prove existence theorems of asymptotic solutions to integrable systems of partial differential equations of the first order with irregular singular points under certain general conditions.
We also prove analytic splitting lemmas for completely inte-
grable linear Pfaffian systems.
Moreover, for integrable connections with irregular
singular points, we formulate and solve the RiemannHilbertBirkhoff problem, and prove analogues of Poincare's lemma and de Rham cohomology theorem under certain general conditions.
Key words and phrases.
Strongly asymptotically developable, strongly asymptotic
expansions of functions of several variables, sheaf of germs of strongly asymptotically developable functions, real blowup of a complex manifold along a normal crossing divisor, vanishing theorem, integrable system of partial differential equations of the first order with regular and irregular singular points, existence theorems of asymptotic solutions to integrable systems with singular points, splitting lemmas for completely integrable Pfaffian systems with singular points, Stokes multipliers, Stokes phenomena, RiemannHilbertBirkhoff problem, Integrable connections with regular and irregular singular points, Vde Rharn complex for inte grable connection V, VPoincare
lemma, Vde Rham cohomology theorem.
Preface The purpose of this paper is tolay a foundation of studies on integrable connections, i.e., locally speaking, completely integrable Pfaffian systems or systems of partial differential equations of the first order, with irregular singular points.
Using strongly asymptotic expansions of functions of several variables,
we prove existence theorems of asymptotic solutions to integrable systems of partial differential equations under certain general conditions.
Moreover, we formu-
late and solve the RiemannHilbertBirkhoff p
Data Loading...
