Topics in operator semigroups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2010
|
| Series: | Progress in mathematics
281 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 266 S. |
| ISBN: | 9780817649319 |
Staff View
MARC
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| 100 | 1 | |a Kantorovitz, Shmuel |d 1935- |e Verfasser |0 (DE-588)132426080 |4 aut | |
| 245 | 1 | 0 | |a Topics in operator semigroups |c Shmuel Kantorovitz |
| 264 | 1 | |a Boston [u.a.] |b Birkhäuser |c 2010 | |
| 300 | |a XIII, 266 S. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
........................................................ xi
Part I General Theory
A. Basic Theory
.............................................. 3
A.I Overview
............................................... 3
A.2 The Generator
.......................................... 5
A.3 Type and Spectrum
...................................... 9
A.4 Uniform Continuity
...................................... 10
A.5 Core for the Generator
................................... 11
A.6 The Resolvent
.......................................... 13
A.7 Pseudo-Resolvents
....................................... 15
A.8 The Laplace Transform
................................... 17
A.9 Abstract Potentials
...................................... 18
A.10 The Hille-Yosida Theorem
................................ 20
A.ll The Hille-Yosida Space
.................................. 22
A.12 Dissipative Operators
.................................... 25
A.
13
The Trotter-Kato Convergence Theorem
................... 28
A.14 Exponential Formulas
.................................... 32
A.15 Perturbation of Generators
............................... 36
A.16 Groups of Operators
..................................... 42
A.17 Bounded Groups of Operators
............................. 43
A.18 Stone s Theorem
........................................ 44
A.19 Bochner s Theorem
...................................... 47
B. The Semi-Simplicity Space for Groups
..................... 49
B.I The Bochner Norm
...................................... 49
B.2 The Semi-Simplicity Space
................................ 53
B.3 Scalar-Type Spectral Operators
........................... 59
viii Contents
C.
Analyticity................................................ 63
C.I Analytic Semigroups
..................................... 63
С.
2
The Generator of an Analytic Semigroup
................... 65
D. The Semigroup as a Function of its Generator
............. 71
D.I
Noncommutative
Taylor Formula
.......................... 71
D.2 Analytic Families of Semigroups
........................... 79
E. Large Parameter
........................................... 87
E.I Analytic Semigroups
..................................... 87
E.2 Resolvent Iterates
....................................... 90
E.3 Mean Stability
.......................................... 94
E.4 The Asymptotic Space
...................................103
E.5 Semigroups of Isometries
.................................107
E.6 The ABLV Stability Theorem
.............................109
F. Boundary Values
..........................................113
F.I Regular Semigroups and Boundary Values
..................113
F.2 The Generator of a Regular Semigroup
.....................118
F.3 Examples of Regular Semigroups
..........................121
G. Pre-Semigroups
............................................131
G.I The Abstract Cauchy Problem
............................132
G.2 The Exponentially Tamed Case
...........................136
Part II Integral Representations
A. The Semi-Simplicity Space
.................................141
A.I The Real Spectrum Case
.................................141
A.2 The Case R+
С
p(-A)...................................
154
B.
The Laplace-Stieltjes Space
...............................161
B.I The Laplace-Stieltjes Space
...............................161
B.2 Semigroups of Closed Operators
...........................166
B.3 The Integrated Laplace Space
.............................169
B.4 Integrated Semigroups
...................................173
C. Families of Unbounded Symmetric Operators
..............177
C.I Local Symmetric Semigroups
..............................177
C.2 Nelson s Analytic Vectors Theorem
........................181
C.3 Local Bounded Below Cosine Families
......................183
C.4 Local Symmetric Cosine Families
..........................187
Contents
Part
III A Taste
of
Applications
A. Analytic Families of Evolution Systems
....................195
A.I Coefficients Analyticity and Solutions Analyticity
............195
A.
2
Kato s Conditions
.......................................196
A.3 Tanabe s Conditions
.....................................198
B. Similarity
..................................................203
B.I Overview
...............................................203
B.2 Similarity Within the Family
S
+
ζν ......................
203
В.
3
Similarity of Certain Perturbations
........................217
Miscellaneous Exercises
........................................219
Notes and References
..........................................249
Bibliography
...................................................253
Index
..........................................................263
|
| any_adam_object | 1 |
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| classification_rvk | SA 1055 SK 620 |
| ctrlnum | (OCoLC)436264806 (DE-599)DNB995196168 |
| dewey-full | 512.27 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.27 |
| dewey-search | 512.27 |
| dewey-sort | 3512.27 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035791118 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:04:39Z |
| institution | BVB |
| isbn | 9780817649319 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018650450 |
| oclc_num | 436264806 |
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| owner | DE-703 DE-11 DE-83 DE-824 DE-355 DE-BY-UBR |
| owner_facet | DE-703 DE-11 DE-83 DE-824 DE-355 DE-BY-UBR |
| physical | XIII, 266 S. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Kantorovitz, Shmuel 1935- Verfasser (DE-588)132426080 aut Topics in operator semigroups Shmuel Kantorovitz Boston [u.a.] Birkhäuser 2010 XIII, 266 S. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 281 Semigroups of operators Spectral theory (Mathematics) Operatorhalbgruppe (DE-588)4172620-0 gnd rswk-swf Operatorhalbgruppe (DE-588)4172620-0 s DE-604 Erscheint auch als Online-Ausgabe 978-0-8176-4932-6 Progress in mathematics 281 (DE-604)BV000004120 281 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018650450&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kantorovitz, Shmuel 1935- Topics in operator semigroups Progress in mathematics Semigroups of operators Spectral theory (Mathematics) Operatorhalbgruppe (DE-588)4172620-0 gnd |
| subject_GND | (DE-588)4172620-0 |
| title | Topics in operator semigroups |
| title_auth | Topics in operator semigroups |
| title_exact_search | Topics in operator semigroups |
| title_full | Topics in operator semigroups Shmuel Kantorovitz |
| title_fullStr | Topics in operator semigroups Shmuel Kantorovitz |
| title_full_unstemmed | Topics in operator semigroups Shmuel Kantorovitz |
| title_short | Topics in operator semigroups |
| title_sort | topics in operator semigroups |
| topic | Semigroups of operators Spectral theory (Mathematics) Operatorhalbgruppe (DE-588)4172620-0 gnd |
| topic_facet | Semigroups of operators Spectral theory (Mathematics) Operatorhalbgruppe |
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