From divergent power series to analytic functions: theory and application of multisummable power series
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1994
|
| Series: | Lecture notes in mathematics
1582 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 106 S. |
| ISBN: | 3540582681 0387582681 |
Staff View
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| 100 | 1 | |a Balser, Werner |d 1946- |e Verfasser |0 (DE-588)121660230 |4 aut | |
| 245 | 1 | 0 | |a From divergent power series to analytic functions |b theory and application of multisummable power series |c Werner Balser |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1994 | |
| 300 | |a X, 106 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1582 | |
| 650 | 7 | |a Asymptotisch gedrag |2 gtt | |
| 650 | 4 | |a Développements asymptotiques | |
| 650 | 4 | |a Fonctions analytiques | |
| 650 | 7 | |a Reeksontwikkelingen |2 gtt | |
| 650 | 4 | |a Sommabilité | |
| 650 | 4 | |a Séries de puissances | |
| 650 | 4 | |a Power series | |
| 650 | 4 | |a Asymptotic expansions | |
| 650 | 4 | |a Summability theory | |
| 650 | 4 | |a Analytic functions | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
1 Asymptotic Power Series 1
1.1 Sectors 1
1.2 Analytic Functions in Sectors 2
1.3 Formal Power Series 4
1.4 Asymptotic Expansions 6
1.5 Gevrey Asymptotics 8
1.6 More on Gevrey Asymptotics 11
2 Laplace and Borel Transforms 13
2.1 Laplace Transforms 13
2.2 Gevrey Asymptotics in Sectors of Small Opening 17
2.3 Borel Transforms 19
2.4 Inversion Formulas 21
3 Summable Power Series 23
3.1 Gevrey Asymptotics in Sectors of Large Opening 23
3.2 Definition of k Summability in a Direction d 24
3.3 The Algebra of k Summable Series in a Direction 28
3.4 Definition of k Summability 29
4 Cauchy Heine Transform 33
4.1 Definition and Basic Properties 33
4.2 Normal Coverings 35
4.3 Decomposition Theorems 36
4.4 A Characterization of Functions with Gevrey Asymptotic 38
5 Acceleration Operators 41
5.1 Definition and Properties of the Kernel 41
5.2 Basic Properties of the Acceleration Operators 43
5.3 Convolutions 47
5.4 Admissible Functions 50
6 Multisummable Power Series 53
6.1 Definition of Multisummability in Directions 53
6.2 Elementary Properties 54
6.3 The Main Decomposition Result 56
6.4 The Algebra of Multisummable Power Series in a Direction 60
X CONTENTS
6.5 Singular Directions 62
6.6 Multisummability 64
6.7 Some Applications of Cauchy Heine Transforms 68
7 Some Equivalent Definitions of Multisummability 75
7.1 An Inductive Definition 75
7.2 Summability through Iterated Laplace Transforms 77
7.3 A Definition via the Sum 79
8 Formal Solutions to Non Linear ODE 83
8.1 Normalizations of the Equation 83
8.2 Formal Iterations 87
8.3 Definition of Admissible Regions 91
8.4 Proper Iterations 94
8.5 The Convergence Proof 98
References 103
Index 107
List of Symbols 108
|
| any_adam_object | 1 |
| author | Balser, Werner 1946- |
| author_GND | (DE-588)121660230 |
| author_facet | Balser, Werner 1946- |
| author_role | aut |
| author_sort | Balser, Werner 1946- |
| author_variant | w b wb |
| building | Verbundindex |
| bvnumber | BV009707072 |
| callnumber-first | Q - Science |
| callnumber-label | QA3 QA295 |
| callnumber-raw | QA3 QA295.L28 no. 1582 |
| callnumber-search | QA3 QA295.L28 no. 1582 |
| callnumber-sort | QA 13 _Q A295 L28 NO 41582 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 850 SK 470 SK 750 |
| classification_tum | MAT 302f MAT 326f |
| ctrlnum | (OCoLC)30734838 (DE-599)BVBBV009707072 |
| dewey-full | 510S515.243220 510 515.2432 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 515 - Analysis |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV009707072 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:39:34Z |
| institution | BVB |
| isbn | 3540582681 0387582681 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006420832 |
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| physical | X, 106 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Balser, Werner 1946- Verfasser (DE-588)121660230 aut From divergent power series to analytic functions theory and application of multisummable power series Werner Balser Berlin [u.a.] Springer 1994 X, 106 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1582 Asymptotisch gedrag gtt Développements asymptotiques Fonctions analytiques Reeksontwikkelingen gtt Sommabilité Séries de puissances Power series Asymptotic expansions Summability theory Analytic functions Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Asymptotische Methode (DE-588)4287476-2 gnd rswk-swf Potenzreihe (DE-588)4138577-9 gnd rswk-swf Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 gnd rswk-swf Asymptotische Entwicklung (DE-588)4112609-9 gnd rswk-swf Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 s Asymptotische Methode (DE-588)4287476-2 s DE-604 Potenzreihe (DE-588)4138577-9 s Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Asymptotische Entwicklung (DE-588)4112609-9 s Lecture notes in mathematics 1582 (DE-604)BV000676446 1582 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006420832&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Balser, Werner 1946- From divergent power series to analytic functions theory and application of multisummable power series Lecture notes in mathematics Asymptotisch gedrag gtt Développements asymptotiques Fonctions analytiques Reeksontwikkelingen gtt Sommabilité Séries de puissances Power series Asymptotic expansions Summability theory Analytic functions Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Asymptotische Methode (DE-588)4287476-2 gnd Potenzreihe (DE-588)4138577-9 gnd Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 gnd Asymptotische Entwicklung (DE-588)4112609-9 gnd |
| subject_GND | (DE-588)4020929-5 (DE-588)4287476-2 (DE-588)4138577-9 (DE-588)4353441-7 (DE-588)4112609-9 |
| title | From divergent power series to analytic functions theory and application of multisummable power series |
| title_auth | From divergent power series to analytic functions theory and application of multisummable power series |
| title_exact_search | From divergent power series to analytic functions theory and application of multisummable power series |
| title_full | From divergent power series to analytic functions theory and application of multisummable power series Werner Balser |
| title_fullStr | From divergent power series to analytic functions theory and application of multisummable power series Werner Balser |
| title_full_unstemmed | From divergent power series to analytic functions theory and application of multisummable power series Werner Balser |
| title_short | From divergent power series to analytic functions |
| title_sort | from divergent power series to analytic functions theory and application of multisummable power series |
| title_sub | theory and application of multisummable power series |
| topic | Asymptotisch gedrag gtt Développements asymptotiques Fonctions analytiques Reeksontwikkelingen gtt Sommabilité Séries de puissances Power series Asymptotic expansions Summability theory Analytic functions Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Asymptotische Methode (DE-588)4287476-2 gnd Potenzreihe (DE-588)4138577-9 gnd Lineare gewöhnliche Differentialgleichung (DE-588)4353441-7 gnd Asymptotische Entwicklung (DE-588)4112609-9 gnd |
| topic_facet | Asymptotisch gedrag Développements asymptotiques Fonctions analytiques Reeksontwikkelingen Sommabilité Séries de puissances Power series Asymptotic expansions Summability theory Analytic functions Gewöhnliche Differentialgleichung Asymptotische Methode Potenzreihe Lineare gewöhnliche Differentialgleichung Asymptotische Entwicklung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006420832&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT balserwerner fromdivergentpowerseriestoanalyticfunctionstheoryandapplicationofmultisummablepowerseries |