Divergent series, summability and resurgence.: II, Simple and multiple summability
(Web Content)
Author:
Series:
Lecture notes in mathematics (Springer-Verlag) ; volume 2154.
Published:
Switzerland : Springer, 2016.
Format:
Web Content
Content Description:
1 online resource (xxiii, 272 pages) : color illustrations.
Status:
Available Online
Description
Addressing the question how to "sum" a power series in one variable when it diverges, that is, how to attach to it analytic functions, the volume gives answers by presenting and comparing the various theories of k-summability and multisummability. These theories apply in particular to all solutions of ordinary differential equations. The volume includes applications, examples and revisits, from a cohomological point of view, the group of tangent-to-identity germs of diffeomorphisms of C studied in volume 1. With a view to applying the theories to solutions of differential equations, a detailed survey of linear ordinary differential equations is provided which includes Gevrey asymptotic expansions, Newton polygons, index theorems and Sibuya?s proof of the meromorphic classification theorem that characterizes the Stokes phenomenon for linear differential equations. This volume is the second of a series of three entitled Divergent Series, Summability and Resurgence. It is aimed at graduate students and researchers in mathematics and theoretical physics who are interested in divergent series, Although closely related to the other two volumes it can be read independently
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Language:
Unknown
ISBN:
9783319290751, 3319290754
UPC:
10.1007/978-3-319-29075-1
Notes
Bibliography
Includes bibliographical references and index.
Description
Addressing the question how to "sum" a power series in one variable when it diverges, that is, how to attach to it analytic functions, the volume gives answers by presenting and comparing the various theories of k-summability and multisummability. These theories apply in particular to all solutions of ordinary differential equations. The volume includes applications, examples and revisits, from a cohomological point of view, the group of tangent-to-identity germs of diffeomorphisms of C studied in volume 1. With a view to applying the theories to solutions of differential equations, a detailed survey of linear ordinary differential equations is provided which includes Gevrey asymptotic expansions, Newton polygons, index theorems and Sibuya?s proof of the meromorphic classification theorem that characterizes the Stokes phenomenon for linear differential equations. This volume is the second of a series of three entitled Divergent Series, Summability and Resurgence. It is aimed at graduate students and researchers in mathematics and theoretical physics who are interested in divergent series, Although closely related to the other two volumes it can be read independently
Language
Foreword in French.
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Citations
APA Citation (style guide)
Loday-Richaud, M. (2016). Divergent series, summability and resurgence. Springer.
Chicago / Turabian - Author Date Citation (style guide)Loday-Richaud, Michèle. 2016. Divergent Series, Summability and Resurgence. Springer.
Chicago / Turabian - Humanities Citation (style guide)Loday-Richaud, Michèle, Divergent Series, Summability and Resurgence. Springer, 2016.
MLA Citation (style guide)Loday-Richaud, Michèle. Divergent Series, Summability and Resurgence. Springer, 2016.
Note! Citation formats are based on standards as of July 2022. Citations contain only title, author, edition, publisher, and year published. Citations should be used as a guideline and should be double checked for accuracy.
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| 505 | 0 | |a Avant-propos -- Preface to the three volumes -- Introduction to this volume -- 1 Asymptotic Expansions in the Complex Domain -- 2 Sheaves and Čech cohomology -- 3 Linear Ordinary Differential Equations -- 4 Irregularity and Gevrey Index Theorems -- 5 Four Equivalent Approaches to k-Summability -- 6 Tangent-to-Identity Diffeomorphisms -- 7 Six Equivalent Approaches to Multisummability -- Exercises -- Solutions to Exercises -- Index -- Glossary of Notations -- References. | |
| 520 | |a Addressing the question how to "sum" a power series in one variable when it diverges, that is, how to attach to it analytic functions, the volume gives answers by presenting and comparing the various theories of k-summability and multisummability. These theories apply in particular to all solutions of ordinary differential equations. The volume includes applications, examples and revisits, from a cohomological point of view, the group of tangent-to-identity germs of diffeomorphisms of C studied in volume 1. With a view to applying the theories to solutions of differential equations, a detailed survey of linear ordinary differential equations is provided which includes Gevrey asymptotic expansions, Newton polygons, index theorems and Sibuya?s proof of the meromorphic classification theorem that characterizes the Stokes phenomenon for linear differential equations. This volume is the second of a series of three entitled Divergent Series, Summability and Resurgence. It is aimed at graduate students and researchers in mathematics and theoretical physics who are interested in divergent series, Although closely related to the other two volumes it can be read independently | ||
| 546 | |a Foreword in French. | ||
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