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D-modules and microlocal calculus

Author: Masaki Kashiwara
Publisher: Providence, R.I. : American Mathematical Society, ©2003.
Series: Translations of mathematical monographs, v. 217.; Iwanami series in modern mathematics.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:

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  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Masaki Kashiwara
ISBN: 0821827669 9780821827666
OCLC Number: 50773693
Description: xvi, 254 p. ; 22 cm.
Contents: 1.2. Differential Homomorphisms of O[subscript X]-modules 2 --
1.3. A System of Generators of D 6 --
1.4. Left D[subscript X]-modules and Right D[subscript X]-modules 7 --
Chapter 2. Characteristic Varieties 11 --
2.1. Cotangent Bundles 11 --
2.2. Characteristic Varieties 15 --
2.3. Involutivity 21 --
2.4. Codimension Filtration 22 --
Chapter 3. Construction of D-modules 29 --
3.1. Tensor Products 29 --
3.2. Homological Properties of D-modules 32 --
3.3. Dual Module 36 --
3.4. Algebraic Relative Cohomology 39 --
Chapter 4. Functorial Properties of D-modules 57 --
4.1. Pull-backs of D-modules 57 --
4.2. Derived Functors of Inverse Images 59 --
4.3. External Tensor Product 60 --
4.4. Coherence of Inverse Images 61 --
4.5. Cauchy-Kovalevskaya Theorem 68 --
4.6. Integrals of D-modules 74 --
4.7. Coherence of Integrals 76 --
4.8. D-modules Supported by a Submanifold 84 --
4.9. Adjunction Formula 87 --
4.10. Adjunction Formula (Inverse Form) 93 --
4.11. Holonomic Systems 94 --
Chapter 5. Regular Holonomic Systems 99 --
5.1. Ordinary Differential Equations with Regular Singularities 99 --
5.2. Holonomic Modules with Regular Singularities 100 --
5.3. Riemann-Hilbert Correspondence 102 --
Chapter 6. b-functions 105 --
6.1. Motivation for b-functions 105 --
6.2. D-module Generated by f(x)[superscript s] 106 --
6.3. Rationality of b-functions 109 --
6.4. b-functions in the Case of Quasi-homogeneous Isolated Singularities 114 --
6.5. b-function and Irreducibility 117 --
Chapter 7. Ring of Formal Microdifferential Operators 123 --
7.1. Microlocalization 123 --
7.2. Formal Microdifferential Operators on Manifolds 125 --
7.3. Microdifferential Operators 129 --
7.4. Algebraic Properties of [varepsilon] 130 --
7.5. Relations between D[subscript X] and [varepsilon subscript X] 139 --
7.6. Involutivity of the Supports of Coherent [varepsilon]-modules 147 --
Chapter 8. Microlocal Analysis of Holonomic Systems 153 --
8.1. Simple [varepsilon]-modules 153 --
8.2. Quantized Contact Transformation 153 --
8.3. Subprincipal Symbols 159 --
8.4. Preparation for the Classification of Simple Holonomic Systems 161 --
8.5. Classification of Simple Holonomic Systems (1) 168 --
8.6. Principal Symbols of Simple Holonomic Modules 170 --
8.7. Regular Holonomic [varepsilon subscript X]-modules 176 --
8.8. Classification of Simple Holonomic Systems (2) 181 --
8.9. Subholonomic Systems 186 --
Chapter 9. Microlocal Calculus of b-functions 191 --
9.1. Microlocal b-functions 191 --
9.2. Existence of Microlocal b-functions 196 --
9.3. Simple Intersection of Lagrangian Analytic Subsets 200 --
9.4. Relation of b-functions of Two Lagrangian Analytic Subsets with a Good Intersection 201 --
9.5. b-functions of Relative Invariants 205 --
A.1. Finiteness of Filtered Rings and Their Modules 213 --
A.2. Derived Categories 226 --
A.3. Derived Functors on Categories of Modules 239 --
A.4. Symplectic Manifolds 243.
Series Title: Translations of mathematical monographs, v. 217.; Iwanami series in modern mathematics.
Other Titles: Daisū kaiseki gairon.
Responsibility: Masaki Kashiwara ; translated by Matsumi Saito.

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