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E-raamat: Fundamentals of Algebraic Microlocal Analysis

(George Mason University, Fairfax, Virginia), (California Polytechnic State University, San Luis Obispo)
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Fundamentals of Algebraic Microlocal AnalysisSuurem pilt
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"Provides a thorough introduction to the algebraic theory of systems of differential equations, as developed by the Japanese school of M. Sato and his colleagues. Features a complete review of hyperfunction-microfunction theory and the theory of D-modules. Strikes the perfect balance between analytic and algebraic aspects."

Arvustused

"...a pleasant introduction to the subject." ---Mathematical Reviews (2000)

Preface v
1 Hyperfunctions
1(90)
1.1 Introduction
1(1)
1.2 Hyperfunctions of One Variable: Basic Definitions
2(18)
1.3 Hyperfunctions of One Variable: Main Results
20(22)
1.4 Hyperfunctions of Several Variables: Basics
42(18)
1.5 Hyperfunctions of Several Variables: Main Results
60(12)
1.6 Historical Notes
72(19)
1.6.1 Sato's Discovery
73(2)
1.6.2 Analytic Functionals
75(4)
1.6.3 Generalized Fourier Integrals
79(1)
1.6.4 Hyperfunctions in Several Variables
80(3)
1.6.5 Infinite Order Differential Equations
83(2)
1.6.6 The Edge of the Wedge Theorem
85(6)
2 Microfunctions
91(60)
2.1 Introduction
91(1)
2.2 Singular Support, Essential Support and Spectrum
92(21)
2.3 Microfunctions of One Variable
113(2)
2.4 Microfunctions of Several Variables
115(7)
2.5 Microlocal Operators
122(12)
2.6 Historical Notes
134(17)
2.6.1 Physical Origins for the Theory of Microfunctions
134(7)
2.6.2 Hormander's Analytic Wave Front Set
141(10)
3 D-Modules
151(32)
3.1 Introduction
151(5)
3.2 Algebraic Geometry and Algebraic Analysis
156(13)
3.3 Filtrations and Characteristic Varieties
169(7)
3.4 Epsilon-Modules
176(3)
3.5 Historical Notes
179(4)
4 Functors Associated with D-modules
183(26)
4.1 Introduction and Preliminary Material
183(4)
4.2 The de Rham Functor
187(13)
4.3 Algebraic Local Cohomology
200(3)
4.4 Cohomological Properties of D(x)
203(6)
5 Holonomic D-modules
209(30)
5.1 Introduction
209(1)
5.2 Inverse Image and Cauchy Problem
209(9)
5.3 Direct Image
218(4)
5.4 Holonomic D-Modules
222(14)
5.5 Historical Notes
236(3)
6 Systems of Microdifferential Equations
239(36)
6.1 Introduction
239(2)
6.2 The Invertibility of Microlocal Operators
241(8)
6.3 A First Approach to Bicharacteristic Strips
249(6)
6.4 Contact Transformations
255(6)
6.5 Structure of Systems of Differential Equations
261(11)
6.6 Historical Notes
272(3)
Bibliography 275(16)
Index 291
Kato\, Goro; Struppa\, Daniele C
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