Divergent Series, Summability and Resurgence II : Simple and Multiple Summability / by Michèle Loday-Richaud.

Format:

Book

Author/Creator:

Loday-Richaud, Michèle., Author.

Series:

Lecture Notes in Mathematics, 0075-8434 ; 2154

Language:

English

Subjects (All):

Sequences (Mathematics).

Differential equations.

Difference equations.

Functional equations.

Dynamics.

Ergodic theory.

Sequences, Series, Summability.

Ordinary Differential Equations.

Difference and Functional Equations.

Dynamical Systems and Ergodic Theory.

Local Subjects:

Sequences, Series, Summability.

Ordinary Differential Equations.

Difference and Functional Equations.

Dynamical Systems and Ergodic Theory.

Physical Description:

1 online resource (XXIII, 272 p. 64 illus. in color.)

Edition:

1st ed. 2016.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2016.

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 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.

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.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

3-319-29075-4

OCLC:

953243796