The asymptotic behaviour of semigroups of linear operators:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Basel [u.a.]
Birkhäuser
1996
|
| Series: | Operator theory
88 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 236 S. |
| ISBN: | 3764354550 0817654550 |
Staff View
MARC
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| 100 | 1 | |a Neerven, Jan van |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The asymptotic behaviour of semigroups of linear operators |c Jan van Neerven |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 1996 | |
| 300 | |a XII, 236 S. | ||
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| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Opérateurs linéaires | |
| 650 | 7 | |a Opérateurs linéaires |2 ram | |
| 650 | 4 | |a Semi-groupes d'opérateurs | |
| 650 | 7 | |a Semigroepen |2 gtt | |
| 650 | 7 | |a Semigroupes d'opérateurs |2 ram | |
| 650 | 7 | |a Semigrupos |2 larpcal | |
| 650 | 4 | |a Équations d'évolution | |
| 650 | 4 | |a Evolution equations | |
| 650 | 4 | |a Linear operators | |
| 650 | 4 | |a Semigroups of operators | |
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Record in the Search Index
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| adam_text | Contents
Chapter 1. Spectral bound and growth bound 1
1.1. Co semigroups and the abstract Cauchy problem 2
1.2. The spectral bound and growth bound of a semigroup 8
1.3. The Laplace transform and its complex inversion 15
1.4. Positive semigroups 19
Notes 23
Chapter 2. Spectral mapping theorems 25
2.1. The spectral mapping theorem for the point spectrum .... 26
2.2. The spectral mapping theorems of Greiner and Gearhart . . 31
2.3. Eventually uniformly continuous semigroups 35
2.4. Groups of non quasianalytic growth 42
2.5. Latushkin Montgomery Smith theory 64
Notes 70
Chapter 3. Uniform exponential stability 73
3.1. The theorem of Datko and Pazy 74
3.2. The theorem of Rolewicz 81
3.3. Characterization by convolutions 83
3.4. Characterization by almost periodic functions 90
3.5. Positive semigroups on Lp spaces 95
3.6. The essential spectrum 107
Notes Ill
Chapter 4. Boundedness of the resolvent 113
4.1. The convexity theorem of Weis and Wrobel 114
4.2. Stability and boundedness of the resolvent 115
4.3. Individual stability in 5 convex Banach spaces 121
4.4. Individual stability in spaces with the analytic RNP . . . .128
4.5. Individual stability in arbitrary Banach spaces 132
4.6. Scalarly integrable semigroups 137
Notes 145
Chapter 5. Countability of the unitary spectrum 149
5.1. The stability theorem of Arendt, Batty, Lyubich, and Vu . . 149
5.2. The Katznelson Tzafriri theorem 163
xii Contents
5.3. The unbounded case 168
5.4. Sets of spectral synthesis 175
5.5. A quantitative stability theorem 179
5.6. A Tauberian theorem for the Laplace transform 188
5.7. The splitting theorem of Glicksberg and DeLeeuw 199
Notes 209
Appendix
Al. Fractional powers 215
A2. Interpolation theory 216
A3. Banach lattices 219
A4. Banach function spaces 221
References 225
Index 235
Symbols 237
|
| any_adam_object | 1 |
| author | Neerven, Jan van |
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| id | DE-604.BV010789043 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:58:56Z |
| institution | BVB |
| isbn | 3764354550 0817654550 |
| language | German |
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| physical | XII, 236 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Operator theory |
| series2 | Operator theory |
| spelling | Neerven, Jan van Verfasser aut The asymptotic behaviour of semigroups of linear operators Jan van Neerven Basel [u.a.] Birkhäuser 1996 XII, 236 S. txt rdacontent n rdamedia nc rdacarrier Operator theory 88 Asymptotisch gedrag gtt Equations d'évolution ram Lineaire operatoren gtt Operadores (teoria) larpcal Opérateurs linéaires Opérateurs linéaires ram Semi-groupes d'opérateurs Semigroepen gtt Semigroupes d'opérateurs ram Semigrupos larpcal Équations d'évolution Evolution equations Linear operators Semigroups of operators Halbgruppe (DE-588)4022990-7 gnd rswk-swf Banach-Raum (DE-588)4004402-6 gnd rswk-swf Linearer Operator (DE-588)4167721-3 gnd rswk-swf Asymptotische Darstellung (DE-588)4003339-9 gnd rswk-swf Banach-Raum (DE-588)4004402-6 s Linearer Operator (DE-588)4167721-3 s Halbgruppe (DE-588)4022990-7 s Asymptotische Darstellung (DE-588)4003339-9 s DE-604 Operator theory 88 (DE-604)BV000000970 88 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007207251&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Neerven, Jan van The asymptotic behaviour of semigroups of linear operators Operator theory Asymptotisch gedrag gtt Equations d'évolution ram Lineaire operatoren gtt Operadores (teoria) larpcal Opérateurs linéaires Opérateurs linéaires ram Semi-groupes d'opérateurs Semigroepen gtt Semigroupes d'opérateurs ram Semigrupos larpcal Équations d'évolution Evolution equations Linear operators Semigroups of operators Halbgruppe (DE-588)4022990-7 gnd Banach-Raum (DE-588)4004402-6 gnd Linearer Operator (DE-588)4167721-3 gnd Asymptotische Darstellung (DE-588)4003339-9 gnd |
| subject_GND | (DE-588)4022990-7 (DE-588)4004402-6 (DE-588)4167721-3 (DE-588)4003339-9 |
| title | The asymptotic behaviour of semigroups of linear operators |
| title_auth | The asymptotic behaviour of semigroups of linear operators |
| title_exact_search | The asymptotic behaviour of semigroups of linear operators |
| title_full | The asymptotic behaviour of semigroups of linear operators Jan van Neerven |
| title_fullStr | The asymptotic behaviour of semigroups of linear operators Jan van Neerven |
| title_full_unstemmed | The asymptotic behaviour of semigroups of linear operators Jan van Neerven |
| title_short | The asymptotic behaviour of semigroups of linear operators |
| title_sort | the asymptotic behaviour of semigroups of linear operators |
| topic | Asymptotisch gedrag gtt Equations d'évolution ram Lineaire operatoren gtt Operadores (teoria) larpcal Opérateurs linéaires Opérateurs linéaires ram Semi-groupes d'opérateurs Semigroepen gtt Semigroupes d'opérateurs ram Semigrupos larpcal Équations d'évolution Evolution equations Linear operators Semigroups of operators Halbgruppe (DE-588)4022990-7 gnd Banach-Raum (DE-588)4004402-6 gnd Linearer Operator (DE-588)4167721-3 gnd Asymptotische Darstellung (DE-588)4003339-9 gnd |
| topic_facet | Asymptotisch gedrag Equations d'évolution Lineaire operatoren Operadores (teoria) Opérateurs linéaires Semi-groupes d'opérateurs Semigroepen Semigroupes d'opérateurs Semigrupos Équations d'évolution Evolution equations Linear operators Semigroups of operators Halbgruppe Banach-Raum Linearer Operator Asymptotische Darstellung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007207251&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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