Opis: Divergent Series, Summability and Resurgence II 2016 - Michele Loday-Richaud

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.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.

Szczegóły: Divergent Series, Summability and Resurgence II 2016 - Michele Loday-Richaud

Tytuł: Divergent Series, Summability and Resurgence II 2016
Autor: Michele Loday-Richaud
Wydawnictwo: Springer Verlag
ISBN: 9783319290744
Rok wydania: 2016
Ilość stron: 295
Oprawa: Miękka
Waga: 0.45 kg

Recenzje: Divergent Series, Summability and Resurgence II 2016 - Michele Loday-Richaud