**Translations of Mathematical Monographs
Iwanami Series in Modern Mathematics**

2003; 254 pp; Softcover

MSC: Primary 32; 58;

**Print ISBN: 978-0-8218-2766-6**

Product Code: MMONO/217

Product Code: MMONO/217

List Price: $66.00

AMS Member Price: $52.80

MAA Member Price: $59.40

**Electronic ISBN: 978-1-4704-4642-0
Product Code: MMONO/217.E**

List Price: $66.00

AMS Member Price: $52.80

MAA Member Price: $59.40

# \(D\)-modules and Microlocal Calculus

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*Masaki Kashiwara*

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.

#### Readership

Graduate students and research mathematicians.

#### Table of Contents

# Table of Contents

## $D$-modules and Microlocal Calculus

- Cover Cover11
- Title page iii4
- Contents v6
- Preface ix10
- Preface to the English edition xi12
- Introduction xiii14
- Basic properties of ๐ท-modules 118
- Characteristic varieties 1128
- Construction of ๐ท-modules 2946
- Functorial properties of ๐ท-modules 5774
- Regular holonomic systems 99116
- ๐-functions 105122
- Ring of formal microdifferential operators 123140
- Microlocal analysis of holonomic systems 153170
- Microlocal calculus of ๐-functions 191208
- Appendix 213230
- Bibliography 247264
- Index 251268
- Index of notations 253270
- Back Cover Back Cover1274