Analytic D-Modules and Applications by Jan-Erik BjörkAnalytic D-Modules and Applications by Jan-Erik Björk

Analytic D-Modules and Applications

byJan-Erik Björk

Paperback | December 15, 2010

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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.
Title:Analytic D-Modules and ApplicationsFormat:PaperbackDimensions:594 pages, 9.61 × 6.69 × 0 inPublished:December 15, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048142385

ISBN - 13:9789048142385

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Table of Contents

Series Editor's Preface. Preface. Introduction. I: The Sheaf x and its Modules. II: Operations on D-Modules. III: Holonomic D-Modules. IV: Deligne Modules. V: Regular Holonomic D-Modules. VI: b-Functions. VII: Distributions and Regular Holonomic Systems. VIII: Microdifferential Operators. Appendix: A:I Derived Categories. A:II Sheaf Theory. A:III Filtered Rings. A:IV Homological Algebra. A:V Complex Analysis. A:VI Analytic Geometry. A:VII Symplectic Analysis. References. List of Notations. Index.