One-parameter semigroups for linear evolution equations:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
New York [u.a.]
Springer
2000
|
| Series: | Graduate texts in mathematics
194 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 553 - 576 |
| Physical Description: | XXI, 586 S. graph. Darst. 25 cm |
| ISBN: | 0387984631 9780387984636 |
Staff View
MARC
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| 245 | 1 | 0 | |a One-parameter semigroups for linear evolution equations |c Klaus-Jochen Engel ... With contributions by S. Brendle ... |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2000 | |
| 300 | |a XXI, 586 S. |b graph. Darst. |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics |v 194 | |
| 500 | |a Literaturverz. S. 553 - 576 | ||
| 650 | 4 | |a Linearer Operator - Einparametrige Halbgruppe - Evolutionsgleichung | |
| 650 | 4 | |a Evolution equations | |
| 650 | 4 | |a Semigroups of operators | |
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Record in the Search Index
| _version_ | 1804127728816881664 |
|---|---|
| adam_text | Contents
Preface
..........................................................................
vii
Prelude
..........................................................................xvii
I.
Linear
Dynamical Systems
.......................................... 1
1.
Cauchy s Functional Equation
........................................ 2
2.
Finite-Dimensional Systems: Matrix Semigroups
................... 6
3.
Uniformly Continuous Operator Semigroups
........................ 14
4.
More Semigroups
...................................................... 24
a. Multiplication Semigroups on
Οο(Ω)
.............................. 24
b.
Multiplication Semigroups on
ЬР(П,
μ) ...........................
30
c.
Translation Semigroups
............................................ 33
5.
Strongly Continuous Semigroups
..................................... 36
a. Basic Properties
.................................................... 37
b. Standard Constructions
............................................ 42
Notes
....................................................................... 46
II. Semigroups, Generators, and Resolvents
......................... 47
1.
Generators of Semigroups and Their Resolvents
.................... 48
2.
Examples Revisited
.................................................... 59
a. Standard Constructions
............................................ 59
b. Standard Examples
................................................. 65
3.
Hille-Yosida Generation Theorems
................................... 70
a. Generation of Groups and Semigroups
............................ 71
b. Dissipative Operators and Contraction Semigroups
............. 82
с
More Examples
..................................................... 89
4.
Special Classes
of Semigroups
........................................ 96
a. Analytic Semigroups
............................................... 96
b. Differentiable
Semigroups
.......................................... 109
c.
Eventually Norm-Continuous Semigroups
........................ 112
d. Eventually Compact Semigroups
.................................. 117
e. Examples
............................................................ 120
5.
Interpolation and Extrapolation Spaces for Semigroups
............ 123
Simon Brendle
a. Sobolev Towers
..................................................... 124
b. Favard and Abstract Holder Spaces
............................... 129
с
Fractional Powers
................................................... 137
6.
Well-Posedness for Evolution Equations
............................. 145
Notes
....................................................................... 154
III. Perturbation and Approximation of Semigroups
...............157
1.
Bounded Perturbations
............................................... 157
2.
Perturbations of Contractive and Analytic Semigroups
............ 169
3.
More Perturbations
.................................................... 182
a. The Perturbation Theorem of Desch-Schappacher
............... 182
b. Comparison of Semigroups
......................................... 192
с
The Perturbation Theorem of Miyadera-Voigt
................... 195
d. Additive Versus Multiplicative Perturbations
.................... 201
4.
Trotter-Kato Approximation Theorems
............................. 205
a. A Technical Tool: Pseudoresolvents
............................... 206
b. The Approximation Theorems
..................................... 209
с
Examples
............................................................ 214
5.
Approximation Formulas
.............................................. 219
a. Chernoff Product Formula
......................................... 219
b. Inversion Formulas
................................................. 231
Notes
....................................................................... 236
IV. Spectral Theory for Semigroups and Generators
...............238
1.
Spectral Theory for Closed Operators
............................... 239
2.
Spectrum of Semigroups and Generators
............................ 250
a. Basic Theory
........................................................ 250
b. Spectrum of Induced Semigroups
................................. 259
с
Spectrum of Periodic Semigroups
................................. 266
3.
Spectral Mapping Theorems
.......................................... 270
a. Examples and Counterexamples
................................... 270
b. Spectral Mapping Theorems for Semigroups
..................... 275
с
Weak Spectral Mapping Theorem for Bounded Groups
......... 283
4.
Spectral Theory and Perturbation
................................... 289
Notes
....................................................................... 293
V. Asymptotics of Semigroups
.........................................295
1.
Stability and Hyperbolicity for Semigroups
......................... 296
a. Stability Concepts
.................................................. 296
b. Characterization of Uniform Exponential Stability
.............. 299
с
Hyperbolic Decompositions
........................................ 305
2.
Compact
Semigroups
.................................................. 308
a. General
Semigroups ................................................
308
b.
Weakly Compact Semigroups
...................................... 312
с
Strongly Compact Semigroups
..................................... 317
3.
Eventually Compact and Quasi-compact Semigroups
.............. 329
4.
Mean Ergodic Semigroups
............................................ 337
Notes
....................................................................... 345
VI. Semigroups Everywhere
.............................................347
1.
Semigroups for Population Equations
................................ 348
a. Semigroup Method for the Cell Equation
......................... 349
b. Intermezzo on Positive Semigroups
............................... 353
c. Asymptotics
for the Cell Equation
................................ 358
Notes
................................................................... 361
2.
Semigroups for the Transport Equation
............................. 361
a. Solution Semigroup for the Reactor Problem
.................... 361
b. Spectral and Asymptotic Behavior
................................ 364
Notes
................................................................... 367
3.
Semigroups for Second-Order Cauchy Problems
.................... 367
a. The State Space X
=
Xf xX
..................................... 369
b. The State Space X
=
X x X
...................................... 372
c.
The State Space X
=
X? x X
..................................... 374
Notes
................................................................... 382
4.
Semigroups for Ordinary Differential Operators
.................... 383
M.
Campiti,
G. Metafune, D.
Pallara,
and
Ş.
Romanelli
a. Nondegenerate Operatore
on R
and R+
.......................... 384
b.
Nondegenerate
Operators on Bounded Intervals
................. 388
с
Degenerate Operators
.............................................. 390
d. Analyticity of Degenerate Semigroups
............................ 400
Notes
................................................................... 403
5.
Semigroups for Partial Differential Operators
....................... 404
Abdelaziz Rhandi
a. Notation and Preliminary Results
................................. 405
b. Elliptic Differential Operators with Constant Coefficients
...... 408
с
Elliptic Differential Operators with Variable Coefficients
........ 411
Notes
................................................................... 419
6.
Semigroups for Delay Differential Equations
........................ 419
a. Well-Posedness of Abstract Delay Differential Equations
....... 420
b. Regularity and Asymptotics
....................................... 424
с
Positivity
for Delay Differential Equations
....................... 428
Notes
................................................................... 435
7.
Semigroups for Volterra Equations
................................... 435
a. Mild and Classical Solutions
....................................... 436
b. Optimal Regularity
................................................. 442
с
Integro-Differential Equations
..................................... 447
Notes
................................................................... 452
8.
Semigroups for Control Theory
....................................... 452
a. Controllability
...................................................... 456
b. Observability
........................................................ 466
с
Stabilizability and Detectability
................................... 468
d. Transfer Functions and Stability
.................................. 473
Notes
................................................................... 476
9.
Semigroups for Nonautonomous Cauchy Problems
................. 477
Roland
Schnaubelt
a. Cauchy Problems and Evolution Families
........................ 477
b. Evolution Semigroups
.............................................. 481
с
Perturbation Theory
................................................ 487
d. Hyperbolic Evolution Families in the Parabolic Case
............ 492
Notes
................................................................... 496
VII. A
Brief History of the Exponential Function
.................... 497
Tanja Hahn
and
Carla Perazzoli
1.
A Bird s-Eye View
..................................................... 497
2.
The Functional Equation
............................................. 500
3.
The Differential Equation
............................................. 502
4.
The Birth of Semigroup Theory
...................................... 506
Appendix
A. A Reminder of Some Functional Analysis
........................... 509
B. A
Reminder of Some Operator Theory
.............................. 515
С
Vector-Valued Integration
............................................ 522
a. The Bochner Integral
............................................... 522
b. The Fourier Transform
............................................. 526
с
The Laplace Transform
............................................. 530
Epilogue
Determinism: Scenes from the Interplay Between
Metaphysics and Mathematics
......................................531
Gregor
Nickel
1.
The Mathematical Structure
......................................... 533
2.
Are Relativity, Quantum Mechanics, and Chaos Deterministic?
... 536
3.
Determinism in Mathematical Science from Newton to Einstein
.. 538
4.
Developments in the Concept of Object from Leibniz to Kant
__ 546
5.
Back to Some Roots of Our Problem: Motion in History
.......... 549
6.
Bibliography and Further Reading
................................... 553
References
......................................................................555
List of Symbols and Abbreviations
.......................................577
Index
............................................................................580
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| id | DE-604.BV013032472 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:37:58Z |
| institution | BVB |
| isbn | 0387984631 9780387984636 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008878473 |
| oclc_num | 245925223 |
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| physical | XXI, 586 S. graph. Darst. 25 cm |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | One-parameter semigroups for linear evolution equations Klaus-Jochen Engel ... With contributions by S. Brendle ... New York [u.a.] Springer 2000 XXI, 586 S. graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 194 Literaturverz. S. 553 - 576 Linearer Operator - Einparametrige Halbgruppe - Evolutionsgleichung Evolution equations Semigroups of operators Halbgruppe (DE-588)4022990-7 gnd rswk-swf Linearer Operator (DE-588)4167721-3 gnd rswk-swf Operatorhalbgruppe (DE-588)4172620-0 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 s Operatorhalbgruppe (DE-588)4172620-0 s DE-604 Linearer Operator (DE-588)4167721-3 s 1\p DE-604 Halbgruppe (DE-588)4022990-7 s 2\p DE-604 Engel, Klaus-Jochen Sonstige (DE-588)112783759 oth Brendle, Simon Sonstige oth Graduate texts in mathematics 194 (DE-604)BV000000067 194 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008878473&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | One-parameter semigroups for linear evolution equations Graduate texts in mathematics Linearer Operator - Einparametrige Halbgruppe - Evolutionsgleichung Evolution equations Semigroups of operators Halbgruppe (DE-588)4022990-7 gnd Linearer Operator (DE-588)4167721-3 gnd Operatorhalbgruppe (DE-588)4172620-0 gnd Evolutionsgleichung (DE-588)4129061-6 gnd |
| subject_GND | (DE-588)4022990-7 (DE-588)4167721-3 (DE-588)4172620-0 (DE-588)4129061-6 |
| title | One-parameter semigroups for linear evolution equations |
| title_auth | One-parameter semigroups for linear evolution equations |
| title_exact_search | One-parameter semigroups for linear evolution equations |
| title_full | One-parameter semigroups for linear evolution equations Klaus-Jochen Engel ... With contributions by S. Brendle ... |
| title_fullStr | One-parameter semigroups for linear evolution equations Klaus-Jochen Engel ... With contributions by S. Brendle ... |
| title_full_unstemmed | One-parameter semigroups for linear evolution equations Klaus-Jochen Engel ... With contributions by S. Brendle ... |
| title_short | One-parameter semigroups for linear evolution equations |
| title_sort | one parameter semigroups for linear evolution equations |
| topic | Linearer Operator - Einparametrige Halbgruppe - Evolutionsgleichung Evolution equations Semigroups of operators Halbgruppe (DE-588)4022990-7 gnd Linearer Operator (DE-588)4167721-3 gnd Operatorhalbgruppe (DE-588)4172620-0 gnd Evolutionsgleichung (DE-588)4129061-6 gnd |
| topic_facet | Linearer Operator - Einparametrige Halbgruppe - Evolutionsgleichung Evolution equations Semigroups of operators Halbgruppe Linearer Operator Operatorhalbgruppe Evolutionsgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008878473&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT engelklausjochen oneparametersemigroupsforlinearevolutionequations AT brendlesimon oneparametersemigroupsforlinearevolutionequations |