Analytic D-Modules and Applications / Edition 1

Analytic D-Modules and Applications / Edition 1

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by Jan-Erik Bjork, Jan-Erik Bjvrk
     
 

This is the first monograph to be published on analytic D-modules and it offers a complete and systematic treatment of the foundations together with a thorough discussion of such modern topics as the Riemann—Hilbert correspondence, Bernstein—Sata polynomials and a large variety of results concerning microdifferential analysis.
Analytic D-module theory

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Overview

This is the first monograph to be published on analytic D-modules and it offers a complete and systematic treatment of the foundations together with a thorough discussion of such modern topics as the Riemann—Hilbert correspondence, Bernstein—Sata polynomials and a large variety of results concerning microdifferential analysis.
Analytic D-module theory studies holomorphic differential systems on complex manifolds. It brings new insight and methods into many areas, such as infinite dimensional representations of Lie groups, asymptotic expansions of hypergeometric functions, intersection cohomology on Kahler manifolds and the calculus of residues in several complex variables.
The book contains seven chapters and has an extensive appendix which is devoted to the most important tools which are used in D-module theory. This includes an account of sheaf theory in the context of derived categories, a detailed study of filtered non-commutative rings and homological algebra, and the basic material in symplectic geometry and stratifications on complex analytic sets.
For graduate students and researchers.

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Product Details

ISBN-13:
9780792321149
Publisher:
Springer Netherlands
Publication date:
01/31/1993
Series:
Mathematics and Its Applications (closed) Series, #247
Edition description:
1993
Pages:
581
Product dimensions:
9.21(w) x 6.14(h) x 1.38(d)

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Table of Contents

Series editor's preface
Preface
Introduction
Ch. IThe sheaf D[subscript X] and its modules
Ch. IIOperations on D-modules
Ch. IIIHolonomic D-modules
Ch. IVDeligne modules
Ch. VRegular holonomic D-modules
Ch. VIb-functions
Ch. VIIDistributions and regular holonomic systems
Ch. VIIIMicrodifferential operators
App. I Derived Categories
App. II Sheaf Theory
App. III Filtered rings
App. IV Homological algebra
App. V Complex analysis
App. VI Analytic geometry
App. VII Symplectic analysis
References
List of notations
Index

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