## Divergent Series, Summability and Resurgence II: Simple and Multiple SummabilityAddressing 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 This volume is the second in a series of three, entitled |

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### Contents

Chapter 1 Asymptotic Expansions in the Complex Domain | 1 |

Chapter 2 Sheaves and Čech Cohomology with an Insight into Asymptotics | 33 |

Basic Facts and Infinitesimal Neighborhoods at an Irregular Singular Point | 63 |

Chapter 4 Irregularity and Gevrey Index Theorems for Linear Differential Operators | 121 |

Chapter 5 Four Equivalent Approaches to KSummability | 133 |

Chapter 6 TangenttoIdentity Diffeomorphisms and the Birkhoff Normalization Theorem | 185 |

Chapter 7 Six Equivalent Approaches to Multisummability | 197 |

Chapter 8 Exercises | 236 |

Chapter 9 Solutions to Exercises | 245 |

264 | |

Glossary of Notations | 268 |

270 | |

### Other editions - View all

Divergent Series, Summability and Resurgence II: Simple and Multiple Summability Michèle Loday-Richaud No preview available - 2016 |