03136nmm a2200409 i 4500991003409299707536cr cn ---mpcbr170809s2016 sz | o j |||| 0|eng d978331929075110.1007/978-3-319-29075-1doib14329359-39ule_instBibl. Dip.le Aggr. Matematica e Fisica - Sez. Matematicaeng515.2423AMS 40-02Loday-Richaud, Michèle730102Divergent Series, summability and resurgence II[e-book] :Simple and multiple summability /by Michèle Loday-RichaudCham :Springer,20161 online resourcetexttxtrdacontentcomputercrdamediaonline resourcecrrdacarrierLecture Notes in Mathematics,0075-8434 ;2154Avant-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 ; ReferencesAddressing 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 independentlyDifference equationsFunctional equationsDynamicsErgodic theoryDifferential equationsSpringer eBooksPrinted edition:9783319290744https://link.springer.com/book/10.1007/978-3-319-29075-1An electronic book accessible through the World Wide Web.b1432935903-03-2209-08-17991003409299707536Divergent Series, Summability and Resurgence II1474446UNISALENTOle01309-08-17m@ -engsz 00