Regular and Irregular Holonomic D-Modules

Informationen zum Autor Masaki Kashiwara is a project professor in the Research Institute for Mathematical Sciences at Kyoto University, Japan. He is an internationally recognized specialist of algebraic analysis, the new branch of mathematics created by Mikio Sato in the 1970s. Klappentext D-module theory is essentially the algebraic study of systems of linear partial differential equations. This book, the first devoted specifically to holonomic D-modules, provides a unified treatment of both regular and irregular D-modules. The authors begin by recalling the main results of the theory of indsheaves and subanalytic sheaves, explaining in detail the operations on D-modules and their tempered holomorphic solutions. As an application, they obtain the Riemann-Hilbert correspondence for regular holonomic D-modules. In the second part of the book the authors do the same for the sheaf of enhanced tempered solutions of (not necessarily regular) holonomic D-modules. Originating from a series of lectures given at the Institut des Hautes Études Scientifiques in Paris, this book is addressed to graduate students and researchers familiar with the language of sheaves and D-modules, in the derived sense. Zusammenfassung The theory of D-modules applies to many areas! including linear PDEs! group representation! algebraic geometry and mathematical physics. This book is the first devoted specifically to the most important variety! holonomic D-modules. It provides a complete unified treatment of the theory of holonomic D-modules! both regular and irregular. Inhaltsverzeichnis Introduction; 1. A review on sheaves and D-modules; 2. Indsheaves; 3. Tempered solutions of D-modules; 4. Regular holonomic D-modules; 5. Indsheaves on bordered spaces; 6. Enhanced indsheaves; 7. Holonomic D-modules; 8. Integral transforms; References; List of notations; Index.

Product details

• Authors: Masaki Kashiwara, Masaki (Kyoto University Kashiwara, Masaki Schapira Kashiwara, Kashiwara Masaki, Pierre Schapira, Pierre (Universite de Paris VI (Pierre et Marie Curie)) Schapira, Schapira Pierre
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Paperback / Softback
• Released: 26.05.2016
• EAN: 9781316613450
• ISBN: 978-1-316-61345-0
• No. of pages: 117
• Series: London Mathematical Society Lecture Note Series; London Mathematical Society Lecture Note Series; London Mathematical Society Le
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Miscellaneous; MATHEMATICS / Differential Equations / General, Differential calculus & equations, Differential calculus and equations