Borel-Laplace transform and asymptotic theory: introduction to resurgent analysis
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| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
CRC Press
1996
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 270 S. graph. Darst. |
| ISBN: | 084939435X |
Internformat
MARC
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| 100 | 1 | |a Sternin, Boris Ju. |d 1939- |e Verfasser |0 (DE-588)120484536 |4 aut | |
| 245 | 1 | 0 | |a Borel-Laplace transform and asymptotic theory |b introduction to resurgent analysis |c Boris Yu. Sternin ; Victor E. Shatalov |
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 1996 | |
| 300 | |a 270 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Gewone differentiaalvergelijkingen |2 gtt | |
| 650 | 7 | |a Laplace-transformaties |2 gtt | |
| 650 | 4 | |a Differential equations |x Asymptotic theory | |
| 650 | 4 | |a Laplace transformation | |
| 650 | 0 | 7 | |a Asymptotische Methode |0 (DE-588)4287476-2 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Šatalov, Viktor E. |d 1945- |e Verfasser |0 (DE-588)120484544 |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804125136109961216 |
|---|---|
| adam_text | Contents
INTRODUCTION. Resurgent Analysis in the Theory of
Differential Equations 1
0.1 Singular Points of Ordinary Differential Equations 1
0.1.1 Classification of singular points 2
0.1.2 The Borel Laplace transform 9
0.1.3 The Euler example 11
0.2 Equations on Infinite Cylinder 16
0.2.1 Modification of the Borel Laplace transform 16
0.2.2 Asymptotics of functions of exponential growth ... 19
0.2.3 Asymptotic expansions of solutions 26
0.3 Semi classical Approximations 33
0.3.1 WKB expansions. Elementary theory 33
0.3.2 Exact WKB approximation (quantum oscillator) . . 37
0.3.3 Asymptotics at infinity (the Airy equation) 47
0.3.4 Concluding remarks 55
CHAPTER I. Borel Laplace Transform 57
1.1 Entire Functions of Exponential Type 57
1.1.1 Main definitions 58
1.1.2 The Borel Laplace transform 61
1.1.3 Examples 65
1.2 Hyperfunctions with Compact Support 65
1.2.1 Main definitions 66
1.2.2 The Borel Laplace transform 72
1.2.3 Examples 74
1.3 Hyperfunctions of Exponential Growth 77
1.3.1 Main definitions 78
1.3.2 The Borel Laplace transform 84
1.3.3 Generalized Hyperfunctions 91
1.3.4 Examples 93
1.4 Microfunctions 95
1.4.1 Endlessly continuable hyperfunctions 96
1.4.2 Microfunctions and their Borel Laplace Transform . 101
1.4.3 Microlocalization 108
1.4.4 Examples Ill
CHAPTER II. Resurgent Analysis 115
2.1 Preliminary Remarks 115
2.2 Resurgent Functions 118
2.2.1 Definition of resurgent function 119
2.2.2 The connection homomorphism and the Stokes
phenomenon 124
2.2.3 Asymptotic expansions 128
2.2.4 Resurgent functions with simple singularities .... 140
2.2.5 Generalizations of the notion of a resurgent function.
Resurgent representation 145
2.3 Investigation Near Focal Points. Legendre Uniformization . 149
2.4 Investigation Near Focal Points. Connection
Homomorphism 156
2.4.1 The monodromy properties of a resurgent function . 156
2.4.2 Alient derivatives 163
2.4.3 Alient differential equations 173
2.4.4 Stokes phenomenon and univaluedness 177
2.5 Examples 178
2.5.1 Resurgent functions of the Airy type 179
2.5.2 Special functions of higher order 184
2.5.3 Cylinder parabolic functions 187
CHAPTER III. Applications 193
3.1 Ordinary Differential Equations 193
3.1.1 Auxiliary statements 195
3.1.2 Reduction to the Volterra equation 198
3.1.3 Analytic continuation of terms of the Neumann series 203
3.1.4 Convergence of the Neumann series 207
3.1.5 Resurgent solutions to ordinary differential
equations 211
3.2 Partial Differential Equations 213
3.2.1 Asymptotic solutions to the Schrodinger equation . 214
3.2.2 General equations with polynomial coefficients . . . 218
3.2.3 Examples 223
3.3 The Saddle Point Method 226
3.3.1 Statement of the Problem 227
3.3.2 One dimensional case 229
3.3.3 Multidimensional case 233
APPENDIX. Integral Transforms of Ramifying Analytic
Functions 237
A.I Integral Transform of Homogeneous Functions 237
A.I.I Definition of the transforms 237
A.1.2 Main theorems 242
A.2 Transforms, Associated with the F transform 243
A.2.1 The ft transform 243
A.2.2 The d/ds transform 246
BIBLIOGRAPHY 253
INDEX 267
|
| any_adam_object | 1 |
| author | Sternin, Boris Ju. 1939- Šatalov, Viktor E. 1945- |
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| dewey-ones | 515 - Analysis |
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| id | DE-604.BV010657124 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:56:45Z |
| institution | BVB |
| isbn | 084939435X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007113563 |
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| owner_facet | DE-12 DE-91G DE-BY-TUM |
| physical | 270 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | CRC Press |
| record_format | marc |
| spelling | Sternin, Boris Ju. 1939- Verfasser (DE-588)120484536 aut Borel-Laplace transform and asymptotic theory introduction to resurgent analysis Boris Yu. Sternin ; Victor E. Shatalov Boca Raton [u.a.] CRC Press 1996 270 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Gewone differentiaalvergelijkingen gtt Laplace-transformaties gtt Differential equations Asymptotic theory Laplace transformation Asymptotische Methode (DE-588)4287476-2 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Asymptotische Methode (DE-588)4287476-2 s DE-604 Šatalov, Viktor E. 1945- Verfasser (DE-588)120484544 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007113563&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Sternin, Boris Ju. 1939- Šatalov, Viktor E. 1945- Borel-Laplace transform and asymptotic theory introduction to resurgent analysis Gewone differentiaalvergelijkingen gtt Laplace-transformaties gtt Differential equations Asymptotic theory Laplace transformation Asymptotische Methode (DE-588)4287476-2 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| subject_GND | (DE-588)4287476-2 (DE-588)4012249-9 |
| title | Borel-Laplace transform and asymptotic theory introduction to resurgent analysis |
| title_auth | Borel-Laplace transform and asymptotic theory introduction to resurgent analysis |
| title_exact_search | Borel-Laplace transform and asymptotic theory introduction to resurgent analysis |
| title_full | Borel-Laplace transform and asymptotic theory introduction to resurgent analysis Boris Yu. Sternin ; Victor E. Shatalov |
| title_fullStr | Borel-Laplace transform and asymptotic theory introduction to resurgent analysis Boris Yu. Sternin ; Victor E. Shatalov |
| title_full_unstemmed | Borel-Laplace transform and asymptotic theory introduction to resurgent analysis Boris Yu. Sternin ; Victor E. Shatalov |
| title_short | Borel-Laplace transform and asymptotic theory |
| title_sort | borel laplace transform and asymptotic theory introduction to resurgent analysis |
| title_sub | introduction to resurgent analysis |
| topic | Gewone differentiaalvergelijkingen gtt Laplace-transformaties gtt Differential equations Asymptotic theory Laplace transformation Asymptotische Methode (DE-588)4287476-2 gnd Differentialgleichung (DE-588)4012249-9 gnd |
| topic_facet | Gewone differentiaalvergelijkingen Laplace-transformaties Differential equations Asymptotic theory Laplace transformation Asymptotische Methode Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007113563&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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