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Divergent series, summability and resurgence. II, Simple and multiple summability

Author: Michèle Loday-Richaud
Publisher: Switzerland : Springer, 2016.
Series: Lecture notes in mathematics (Springer-Verlag), 2154.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: (OCoLC)932096085
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Michèle Loday-Richaud
ISBN: 9783319290751 3319290754
OCLC Number: 953243796
Language Note: Foreword in French.
Description: 1 online resource (xxiii, 272 pages) : color illustrations.
Contents: 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.
Series Title: Lecture notes in mathematics (Springer-Verlag), 2154.
Other Titles: Simple and multiple summability
Responsibility: Michèle Loday-Richaud.

Abstract:

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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