Lecture Notes in Mathematics

Divergent Series, Summability and Resurgence II

Simple and Multiple Summability

Authors: Loday-Richaud, Michèle

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  • Provides a thorough discussion and comparison of the theories of k-summability and multisummability
  • Can be treated both as a reference book and as a tutorial on the theories of summability and their links to the formal and local analytic aspects of linear ordinary differential equations
  • Includes a discussion of the linear Stokes phenomenon
  • The theories are illustrated with many examples and over 70 color figures
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  • ISBN 978-3-319-29075-1
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Softcover $59.99
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About this book

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 (9 chapters)

Table of contents (9 chapters)
  • Asymptotic Expansions in the Complex Domain

    Pages 1-31

    Loday-Richaud, Michèle

  • Sheaves and Čech Cohomology with an Insight into Asymptotics

    Pages 33-62

    Loday-Richaud, Michèle

  • Linear Ordinary Differential Equations: Basic Facts and Infinitesimal Neighborhoods at an Irregular Singular Point

    Pages 63-120

    Loday-Richaud, Michèle

  • Irregularity and Gevrey Index Theorems for Linear Differential Operators

    Pages 121-132

    Loday-Richaud, Michèle

  • Four Equivalent Approaches to k-Summability

    Pages 133-183

    Loday-Richaud, Michèle

Buy this book

eBook $44.99
price for USA in USD
  • ISBN 978-3-319-29075-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-3-319-29074-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Divergent Series, Summability and Resurgence II
Book Subtitle
Simple and Multiple Summability
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2154
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-29075-1
DOI
10.1007/978-3-319-29075-1
Softcover ISBN
978-3-319-29074-4
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XXIII, 272
Number of Illustrations
64 illustrations in colour
Topics