Regular And Irregular Holonomic D Modules
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Regular And Irregular Holonomic D Modules
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Author : Masaki Kashiwara
language : en
Publisher: Cambridge University Press
Release Date : 2016-05-26
Regular And Irregular Holonomic D Modules written by Masaki Kashiwara and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-26 with Mathematics categories.
A unified treatment of the Riemann-Hilbert correspondence for (not necessarily regular) holonomic D-modules using indsheaves.
Algebraic Approach To Differential Equations
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Author : Dung Trang Le
language : en
Publisher: World Scientific
Release Date : 2010-05-18
Algebraic Approach To Differential Equations written by Dung Trang Le and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-18 with Mathematics categories.
Mixing elementary results and advanced methods, Algebraic Approach to Differential Equations aims to accustom differential equation specialists to algebraic methods in this area of interest. It presents material from a school organized by The Abdus Salam International Centre for Theoretical Physics (ICTP), the Bibliotheca Alexandrina, and the International Centre for Pure and Applied Mathematics (CIMPA).
Stokes Structure And Direct Image Of Irregular Singular D Modules
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Author : Hedwig Heizinger
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2015-08-10
Stokes Structure And Direct Image Of Irregular Singular D Modules written by Hedwig Heizinger and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-10 with Mathematics categories.
In this thesis we develop a way of examining the Stokes structure of certain irregular singular D-modules, namely the direct image of exponentially twisted meromorphic connections with regular singularities, in a topological point of view. We use this topological description to compute linear Stokes data for an explicit example.
Analytic D Modules And Applications
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Author : Jan-Erik Björk
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Analytic D Modules And Applications written by Jan-Erik Björk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
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.
Abelian Groups And Noncommutative Rings A Collection Of Papers In Memory Of Robert B Warfield Jr
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Author : László Fuchs
language : en
Publisher: American Mathematical Soc.
Release Date : 1992
Abelian Groups And Noncommutative Rings A Collection Of Papers In Memory Of Robert B Warfield Jr written by László Fuchs and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
This collection of research papers is dedicated to the memory of the distinguished algebraist Robert B. Warfield, Jr. Focusing on abelian group theory and noncommutative ring theory, the book covers a wide range of topics reflecting Warfield's interests and includes two articles surveying his contributions to mathematics. Because the articles have been refereed to high standards and will not appear elsewhere, this volume is indispensable to any researcher in noncommutative ring theory or abelian group theory. With papers by some of the major leaders in the field, this book will also be important to anyone interested in these areas, as it provides an overview of current research directions.
Mixed Twistor D Modules
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Author : Takuro Mochizuki
language : en
Publisher: Springer
Release Date : 2015-08-19
Mixed Twistor D Modules written by Takuro Mochizuki and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-19 with Mathematics categories.
We introduce mixed twistor D-modules and establish their fundamental functorial properties. We also prove that they can be described as the gluing of admissible variations of mixed twistor structures. In a sense, mixed twistor D-modules can be regarded as a twistor version of M. Saito's mixed Hodge modules. Alternatively, they can be viewed as a mixed version of the pure twistor D-modules studied by C. Sabbah and the author. The theory of mixed twistor D-modules is one of the ultimate goals in the study suggested by Simpson's Meta Theorem and it would form a foundation for the Hodge theory of holonomic D-modules which are not necessarily regular singular.
Algebraic And Analytic Microlocal Analysis
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Author : Michael Hitrik
language : en
Publisher: Springer
Release Date : 2018-12-19
Algebraic And Analytic Microlocal Analysis written by Michael Hitrik and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-19 with Mathematics categories.
This book presents contributions from two workshops in algebraic and analytic microlocal analysis that took place in 2012 and 2013 at Northwestern University. Featured papers expand on mini-courses and talks ranging from foundational material to advanced research-level papers, and new applications in symplectic geometry, mathematical physics, partial differential equations, and complex analysis are discussed in detail. Topics include Procesi bundles and symplectic reflection algebras, microlocal condition for non-displaceability, polarized complex manifolds, nodal sets of Laplace eigenfunctions, geodesics in the space of Kӓhler metrics, and partial Bergman kernels. This volume is a valuable resource for graduate students and researchers in mathematics interested in understanding microlocal analysis and learning about recent research in the area.
Lectures On Orthogonal Polynomials And Special Functions
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Author : Howard S. Cohl
language : en
Publisher: Cambridge University Press
Release Date : 2020-10-15
Lectures On Orthogonal Polynomials And Special Functions written by Howard S. Cohl and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-15 with Mathematics categories.
Contains graduate-level introductions by international experts to five areas of research in orthogonal polynomials and special functions.
Introduction To Stokes Structures
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Author : Claude Sabbah
language : en
Publisher: Springer
Release Date : 2012-10-03
Introduction To Stokes Structures written by Claude Sabbah and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-03 with Mathematics categories.
This research monograph provides a geometric description of holonomic differential systems in one or more variables. Stokes matrices form the extended monodromy data for a linear differential equation of one complex variable near an irregular singular point. The present volume presents the approach in terms of Stokes filtrations. For linear differential equations on a Riemann surface, it also develops the related notion of a Stokes-perverse sheaf. This point of view is generalized to holonomic systems of linear differential equations in the complex domain, and a general Riemann-Hilbert correspondence is proved for vector bundles with meromorphic connections on a complex manifold. Applications to the distributions solutions to such systems are also discussed, and various operations on Stokes-filtered local systems are analyzed.
D Modules And Microlocal Calculus
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Author : Masaki Kashiwara
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
D Modules And Microlocal Calculus written by Masaki Kashiwara and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
The original title of this work translated as "Foundation of Algebraic Analysis." Kashiwara (Kyoto U., Japan) changed the title to more precisely reflect the nature of the text's contents and to signal his belief that "the microlocal point of view helps concrete calculations, as powerfully as the Cauchy integral formula provides the values of many definite integrals." Chapters cover basic properties of D-modules, characteristic varieties, construction of D-modules, their functorial properties, regular holonomic systems, b-functions, ring of formal microdifferential operators, microlocal analysis of holonomic systems, and microlocal calculus of b-functions. Translated from the Japanese work Daisu Kaiseki Gairon (2000). Annotation copyrighted by Book News, Inc., Portland, OR