Format:
Online-Ressource (XXIII, 272 p. 64 illus. in color, online resource)
ISBN:
9783319290751
Series Statement:
Lecture Notes in Mathematics 2154
Content:
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.
Content:
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.
Additional Edition:
ISBN 9783319290744
Additional Edition:
Erscheint auch als Druck-Ausgabe Loday-Richaud, Michèle Divergent series, summability and resurgence ; 2: Simple and multiple summability [Cham] : Springer International Publishing Switzerland, 2016 ISBN 9783319290744
Language:
English
Subjects:
Mathematics
DOI:
10.1007/978-3-319-29075-1
URL:
Volltext
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URL:
Volltext
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