Simple and multiple summability

Bibliographic Information

Simple and multiple summability

Michèle Loday-Richaud

(Lecture notes in mathematics, 2154 . Divergent series, summability and resurgence ; 2)

Springer, c2016

Available at  / 42 libraries

Search this Book/Journal

Note

Includes bibliographical references (p. 265-267) and index

Description and Table of Contents

Description

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.

Table of Contents

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.

by "Nielsen BookData"

Related Books: 1-1 of 1

Details

  • NCID
    BB2170947X
  • ISBN
    • 9783319290744
  • LCCN
    2016940058
  • Country Code
    sz
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Switzerland
  • Pages/Volumes
    xxiii, 272 p.
  • Size
    24 cm
  • Subject Headings
  • Parent Bibliography ID
Page Top