Divergent series, summability and resurgence II: simple and multiple summability
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
[Cham]
Springer
[2016]
|
| Schriftenreihe: | Lecture notes in mathematics
2154 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xxiii, 272 Seiten Diagramme |
| ISBN: | 9783319290744 |
| ISSN: | 0075-8434 |
Internformat
MARC
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| 650 | 4 | |a Ergodic theory | |
| 650 | 4 | |a Differential equations | |
| 650 | 4 | |a Sequences (Mathematics) | |
| 650 | 4 | |a Sequences, Series, Summability | |
| 650 | 4 | |a Ordinary Differential Equations | |
| 650 | 4 | |a Difference and Functional Equations | |
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Datensatz im Suchindex
| _version_ | 1804176443780890624 |
|---|---|
| adam_text | Michele Loday-Richaud
Divergent Series,
Summability and
Resurgence II
Simple and Multiple Summability
Springer
Contents
Avant-Propos vii
Preface to the Three Volumes ix
Introduction to this Volume xvii
1 Asymptotic Expansions in the Complex Domain 1
1 1 Poincare asymptotics 2
111 Definition 2
112 Examples 3
113 Algebras of Asymptotic Functions 11
1 2 Gevrey Asymptotics 13
121 Gevrey Series 14
122 Algebras of Gevrey Asymptotic Functions 16
123 Flat s-Gevrey Asymptotic Functions 20
1 3 The Borel-Ritt Theorem 21
1 4 The Cauchy-Heine Theorem 26
2 Sheaves and Cech Cohomology 33
2 1 Presheaves and sheaves 33
211 Presheaves 33
212 Sheaves 37
213 From Presheaves to Sheaves: Espaces Etales 37
214 Morphisms of Sheaves 39
215 Sheaves srf of Asymptotic and s4s of s-Gevrey Asymptotic
Functions over S1 41
216 Quotient Sheaves and Exact Sequences 43
217 The Borel-Ritt Theorem Revisited 46
218 Change of Base Space: Direct Image, Restriction and
Extension by 0 46
2 2 Abelian Cech Cohomology 49
XXI
xxii Conten
221 Cohomology of a Covering 4
222 Cohomology of a Space 51
223 The Borel-Ritt Theorem and Cohomology 52
224 The Space S1 and the Cauchy-Heine Theorem 53
2 3 Non-abelian Cech Cohomology 57
231 Non-abelian Cohomology in Degree 0 57
232 Non-abelian Cohomology in Degree 1 581
233 Exact Sequences 60
3 Linear Ordinary Differential Equations 63
3 1 Equation versus System 64
3 2 The Viewpoint of ^-Modules 65
321 ^-Modules and First Order Differential Systems 65
322 ^-Modules and Order n Differential Operators 69
3 3 Formal Meromorphic Classification 71
331 The System Case 71
332 Some Definitions Related to Normal Forms 75
333 The Equation Case 79
3 4 The Main Asymptotic Existence Theorem 86
3 5 Meromorphic Classification 90
351 The Infinitesimal Isomorphism 93
352 Malgrange-Sibuya Theorems 95
353 The Stokes Cocycle Theorem 98
354 Sibuya’s Proof of the Malgrange-Sibuya Isomorphism
Theorem 107
3 6 Infinitesimal neighborhoods 114
361 Infinitesimal Neighborhoods Associated with the
Exponential Order 114
362 Infinitesimal Neighborhoods Associated with the
Exponential Order and Type 117
363 More Infinitesimal Neighborhoods 120
4 Irregularity and Gevrey Index Theorems 121
4 1 Introduction 121
4 2 The Deligne-Malgrange Approach 123
4 3 Wild Analytic Continuation and Index Theorems 131
5 Four Equivalent Approaches to A Summability 133
5 1 The First Approach: Ramis fc-Summability 134
5 2 The Second Approach: Ramis-Sibuya fc-Summability 139
521 Definition 140
522 Applications to Differential Equations 141
5 3 The Third Approach: Borel-Laplace Summation 144
531 Definitions 145
532 Nevanlinna’s Theorem and Summability 154
Contents xxiii
533 Tauberian Theorems 166
534 The Borel-Laplace Summability and the Summable-
Resurgence 175
5 4 The Fourth Approach: Wild Analytic Continuation 180
541 A:-Wild-Summability 180
542 Applications 181
6 Tangent-to-Identity Diffeomorphisms 185
6 1 Introduction 185
6 2 The Birkhoff-Kimura Sectorial Normalization theorem 188
6 3 The Invariance Equation of g v 193
6 4 1-Summability of the Conjugation Series h 194
7 Six Equivalent Approaches to Multisummability 197
7 1 Introduction and the Ramis-Sibuya Series 197
7 2 The First Approach: Asymptotic Definition 200
721 The Relative Watson’s Lemma 200
722 An Asymptotic Definition of Multisummablilty 204
7 3 The Second Approach: Malgrange-Ramis Definition 208
731 Definition 209
732 Application to Differential Equations 210
7 4 The Third Approach: Iterated Laplace Integrals 211
7 5 The Fourth Approach: Balser’s Decomposition into Sums 219
751 The Case ky 1/2 219
752 The Case *i 1/2 221
7 6 The Fifth Approach: ficalle’s Acceleration 223
7 7 The Sixth Approach: Wild Analytic Continuation 231
771 k-Wild-Summability 231
772 Application to Tauberian Theorems 233
Exercises 237
Solutions to Exercises 245
References 265
Glossary of Notations 269
|
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| issn | 0075-8434 |
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| series2 | Lecture notes in mathematics |
| spelling | Loday, Michèle Verfasser aut Divergent series, summability and resurgence II simple and multiple summability Michèle Loday-Richaud [Cham] Springer [2016] xxiii, 272 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 2154 0075-8434 Mathematics Difference equations Functional equations Dynamics Ergodic theory Differential equations Sequences (Mathematics) Sequences, Series, Summability Ordinary Differential Equations Difference and Functional Equations Dynamical Systems and Ergodic Theory Mathematik Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 s DE-604 Erscheint auch als Online-Ausgabe 978-3-319-29075-1 Lecture notes in mathematics 2154 (DE-604)BV000676446 2154 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029091258&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Loday, Michèle Divergent series, summability and resurgence II simple and multiple summability Lecture notes in mathematics Mathematics Difference equations Functional equations Dynamics Ergodic theory Differential equations Sequences (Mathematics) Sequences, Series, Summability Ordinary Differential Equations Difference and Functional Equations Dynamical Systems and Ergodic Theory Mathematik Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| subject_GND | (DE-588)4020929-5 |
| title | Divergent series, summability and resurgence II simple and multiple summability |
| title_auth | Divergent series, summability and resurgence II simple and multiple summability |
| title_exact_search | Divergent series, summability and resurgence II simple and multiple summability |
| title_full | Divergent series, summability and resurgence II simple and multiple summability Michèle Loday-Richaud |
| title_fullStr | Divergent series, summability and resurgence II simple and multiple summability Michèle Loday-Richaud |
| title_full_unstemmed | Divergent series, summability and resurgence II simple and multiple summability Michèle Loday-Richaud |
| title_short | Divergent series, summability and resurgence II |
| title_sort | divergent series summability and resurgence ii simple and multiple summability |
| title_sub | simple and multiple summability |
| topic | Mathematics Difference equations Functional equations Dynamics Ergodic theory Differential equations Sequences (Mathematics) Sequences, Series, Summability Ordinary Differential Equations Difference and Functional Equations Dynamical Systems and Ergodic Theory Mathematik Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd |
| topic_facet | Mathematics Difference equations Functional equations Dynamics Ergodic theory Differential equations Sequences (Mathematics) Sequences, Series, Summability Ordinary Differential Equations Difference and Functional Equations Dynamical Systems and Ergodic Theory Mathematik Gewöhnliche Differentialgleichung |
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