Linear differential equations in the complex domain : problems of analytic continuation / Yasutaka SibuyaType de document : MonographieCollection : Translations of mathematical monographs, 82Langue : anglais.Pays : Etats Unis.Éditeur : Providence : American Mathematical Society, 1990Description : 1 vol. (XIV- 267 p.) : ill. ; 24 cmISBN : 0821845357.ISSN : 0065-9282.Bibliographie : Bibliogr. p. 257-263. Index.Sujet MSC : 34Mxx, Ordinary differential equations - Ordinary differential equations in the complex domain
32D20, Several complex variables and analytic spaces - Analytic continuation, Removable singularities in several complex variables
34-02, Research exposition (monographs, survey articles) pertaining to ordinary differential equationsEn-ligne : MathSciNet | AMS
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Bibliogr. p. 257-263. Index
The main part of this book is a translation of a 1976 book originally written in Japanese. The book, focusing attention on intrinsic aspects of the subject, explores some problems of linear ordinary differential equations in complex domains. Examples of the problems discussed include the Riemann problem on the Riemann sphere, a characterization of regular singularities, and a classification of meromorphic differential equations. Since the original book was published, many new ideas have developed, such as applications of D-modules, Gevrey asymptotics, cohomological methods, k-summability, and studies of differential equations containing parameters. Five appendices, added in the present edition, briefly cover these new ideas. In addition, more than 100 references have been added.
This book will introduce readers to the essential facts concerning the structure of solutions of linear differential equations in the complex domain, as well as illuminate the intrinsic meaning of older results by means of more modern ideas. A useful reference for research mathematicians on various fundamental results, this book would also be suitable as a textbook in a graduate course or seminar. (source : AMS)