Softcover ISBN:  9780821827666 
Product Code:  MMONO/217 
List Price:  $66.00 
MAA Member Price:  $59.40 
AMS Member Price:  $52.80 
Electronic ISBN:  9781470446420 
Product Code:  MMONO/217.E 
List Price:  $66.00 
MAA Member Price:  $59.40 
AMS Member Price:  $52.80 

Book DetailsTranslations of Mathematical MonographsIwanami Series in Modern MathematicsVolume: 217; 2003; 254 ppMSC: Primary 32; 58;
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 twodecade interval has given Kashiwara a very good perspective for presenting the topic to the general mathematical public.ReadershipGraduate students and research mathematicians.

Table of Contents

Chapters

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


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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 twodecade interval has given Kashiwara a very good perspective for presenting the topic to the general mathematical public.
Graduate students and research mathematicians.

Chapters

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