D-modules and microlocal calculus
Author(s)
Bibliographic Information
D-modules and microlocal calculus
（Translations of mathematical monographs, v. 217）（Iwanami series in modern mathematics）
American Mathematical Society, c2003
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代数解析概論
Available at / 40 libraries
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC21:516.36/K1512070577316
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Note
Originally published: Tokyo : Iwanami Shoten, 2000
Includes bibliographical references (p. 247-249) and indexes
Description and Table of Contents
Description
Masaki Kashiwara is undoubtedly one of the masters of the theory of $D$-modules, and he has created a good, accessible entry point to the subject. The theory of $D$-modules is a very powerful point of view, bringing ideas from algebra and algebraic geometry to the analysis of systems of differential equations. It is often used in conjunction with microlocal analysis, as some of the important theorems are best stated or proved using these techniques. The theory has been used very successfully in applications to representation theory.Here, there is an emphasis on $b$-functions. These show up in various contexts: number theory, analysis, representation theory, and the geometry and invariants of prehomogeneous vector spaces. Some of the most important results on $b$-functions were obtained by Kashiwara. A hot topic from the mid '70s to mid '80s, it has now moved a bit more into the mainstream. Graduate students and research mathematicians will find that working on the subject in the two-decade interval has given Kashiwara a very good perspective for presenting the topic to the general mathematical public.
Table of Contents
Basic properties of $D$-modules Characteristic varieties Construction of $D$-modules Functorial properties of $D$-modules Regular holonomic systems $b$-functions Ring of formal microdifferential operators Microlocal analysis of holonomic systems Microlocal calculus of $b$-functions Appendix Bibliography Index Index of notations.
by "Nielsen BookData"