Divergent Series, Summability and Resurgence II

Simple and Multiple Summability
1. Auflage 2016
ISBN: 978-3-319-29074-4
Verlag: Springer International Publishing

Buch, Englisch, Band 2154, 272 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 4511 g

Reihe: Lecture Notes in Mathematics

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 in 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.

Zielgruppe

Research

Autoren/Hrsg.

Loday-Richaud, Michèle

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

Avant-propos.- Preface to the three volumes.- Introduction to this volume.- 1 Asymptotic Expansions in the Complex Domain.- 2 Sheaves and Cech 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.