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$D$-modules and Microlocal Calculus
 
Masaki Kashiwara RIMS, Kyoto University, Kyoto, Japan
D-modules and Microlocal Calculus
D-modules and Microlocal Calculus
Softcover ISBN:  978-0-8218-2766-6
Product Code:  MMONO/217
List Price: $52.00
MAA Member Price: $46.80
AMS Member Price: $41.60
eBook ISBN:  978-1-4704-4642-0
Product Code:  MMONO/217.E
List Price: $49.00
MAA Member Price: $44.10
AMS Member Price: $39.20
Softcover ISBN:  978-0-8218-2766-6
eBook: ISBN:  978-1-4704-4642-0
Product Code:  MMONO/217.B
List Price: $101.00 $76.50
MAA Member Price: $90.90 $68.85
AMS Member Price: $80.80 $61.20
D-modules and Microlocal Calculus
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D-modules and Microlocal Calculus
$D$-modules and Microlocal Calculus
Masaki Kashiwara RIMS, Kyoto University, Kyoto, Japan
Softcover ISBN:  978-0-8218-2766-6
Product Code:  MMONO/217
List Price: $52.00
MAA Member Price: $46.80
AMS Member Price: $41.60
eBook ISBN:  978-1-4704-4642-0
Product Code:  MMONO/217.E
List Price: $49.00
MAA Member Price: $44.10
AMS Member Price: $39.20
Softcover ISBN:  978-0-8218-2766-6
eBook ISBN:  978-1-4704-4642-0
Product Code:  MMONO/217.B
List Price: $101.00 $76.50
MAA Member Price: $90.90 $68.85
AMS Member Price: $80.80 $61.20
  • Book Details
     
     
    Translations of Mathematical Monographs
    Iwanami Series in Modern Mathematics
    Volume: 2172003; 254 pp
    MSC: 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 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
     
     
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Iwanami Series in Modern Mathematics
Volume: 2172003; 254 pp
MSC: 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 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.

  • 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.