TY  - BOOK
AU  - Loday-Richaud,Michèle
ED  - SpringerLink (Online service)
TI  - Divergent Series, Summability and Resurgence II: Simple and Multiple Summability 
T2  - Lecture Notes in Mathematics,
SN  - 9783319290751
AV  - QA292 
U1  - 515.24 23
PY  - 2016///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Sequences (Mathematics)
KW  - Differential Equations
KW  - Functional equations
KW  - Differentiable dynamical systems
KW  - Sequences, Series, Summability
KW  - Ordinary Differential Equations
KW  - Difference and Functional Equations
KW  - Dynamical Systems and Ergodic Theory
N1  - 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
N2  - 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
UR  - https://doi.org/10.1007/978-3-319-29075-1
ER  -