Linear operators and their spectra:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2007
|
| Edition: | 1. publ. |
| Series: | Cambridge studies in advanced mathematics
106 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 436 - 445 |
| Physical Description: | XII, 451 S. graph. Darst. |
| ISBN: | 9780521866293 |
Staff View
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| 245 | 1 | 0 | |a Linear operators and their spectra |c E. Brian Davies |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2007 | |
| 300 | |a XII, 451 S. |b graph. Darst. | ||
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| 490 | 1 | |a Cambridge studies in advanced mathematics |v 106 | |
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Record in the Search Index
| _version_ | 1804136629271527424 |
|---|---|
| adam_text | Contents
Preface
page
ix
1
Elementary operator theory
1
1.1
Banach spaces
1
1.2
Bounded linear operators
12
1.3
Topologies on vector spaces
19
1.4
Differentiation of vector-valued functions
23
1.5
The holomorphic functional calculus
27
2
Function spaces
35
2.1
U
spaces
35
2.2
Operators acting on
U
spaces
45
2.3
Approximation and regularization
54
2.4
Absolutely convergent Fourier series
60
3
Fourier transforms and bases
67
3.1
The Fourier transform
67
3.2
Sobolev spaces
77
3.3
Bases of Banach spaces
80
3.4
Unconditional bases
90
4
Intermediate operator theory
99
4.1
The spectral radius
99
4.2
Compact linear operators
102
4.3
Fredholm
operators
116
4.4
Finding the essential spectrum
124
vi
Contents
5 Operators
on Hubert space
135
5.1
Bounded operators
135
5.2
Polar decompositions
137
5.3
Orthogonal projections
140
5.4
The spectral theorem
143
5.5
Hilbert-Schmidt operators
151
5.6
Trace class operators
153
5.7
The compactness of f{Q)g{P)
160
6
One-parameter semigroups
163
6.1
Basic properties of semigroups
163
6.2
Other continuity conditions
177
6.3
Some standard examples
182
7
Special classes of semigroup
190
7.1
Norm continuity
190
7.2
Trace class semigroups
194
7.3
Semigroups on dual spaces
197
7.4
Differentiable and analytic vectors
201
7.5
Subordinated semigroups
205
8
Resolvents and generators
210
8.1
Elementary properties of resolvents
210
8.2
Resolvents and semigroups
218
8.3
Classification of generators
227
8.4
Bounded holomorphic semigroups
237
9
Quantitative bounds on operators
245
9.1
Pseudospectra
245
9.2
Generalized spectra and pseudospectra
251
9.3
The numerical range
264
9.4
Higher order hulls and ranges
276
9.5 Von
Neumann s theorem
285
9.6
Peripheral point spectrum
287
10
Quantitative bounds on semigroups
296
10.1
Long time growth bounds
296
10.2
Short time growth bounds
300
10.3
Contractions and dilations
307
10.4
The Cayley transform
310
Contents
vii
10.5
One-parameter groups
315
10.6
Resolvent bounds in Hilbert space
321
11
Perturbation theory
325
11.1
Perturbations of unbounded operators
325
11.2
Relatively compact perturbations
330
11.3
Constant coefficient differential operators on the
half-line
335
11.4
Perturbations: semigroup based methods
339
11.5
Perturbations: resolvent based methods
350
12
Markov chains and graphs
355
12.1
Definition of Markov operators
355
12.2
Irreducibility and spectrum
359
12.3
Continuous time Markov chains
362
12.4
Reversible Markov semigroups
366
12.5
Recurrence and transience
369
12.6
Spectral theory of graphs
374
13
Positive semigroups
380
13.1
Aspects of
positivity
380
13.2
Invariant subsets
386
13.3
Irreducibility
390
13.4
Renormalization
393
13.5
Ergodic theory
395
13.6
Positive semigroups on C(X)
399
14 NSA Schrödinger
operators
408
14.1
Introduction
408
14.2
Bounds on the numerical range
409
14.3
Bounds in one space dimension
412
14.4
The essential spectrum of
Schrödinger
operators
420
14.5
The NSA harmonic oscillator
424
14.6
Semi-classical analysis
427
References
436
Index
446
|
| adam_txt |
Contents
Preface
page
ix
1
Elementary operator theory
1
1.1
Banach spaces
1
1.2
Bounded linear operators
12
1.3
Topologies on vector spaces
19
1.4
Differentiation of vector-valued functions
23
1.5
The holomorphic functional calculus
27
2
Function spaces
35
2.1
U
spaces
35
2.2
Operators acting on
U
spaces
45
2.3
Approximation and regularization
54
2.4
Absolutely convergent Fourier series
60
3
Fourier transforms and bases
67
3.1
The Fourier transform
67
3.2
Sobolev spaces
77
3.3
Bases of Banach spaces
80
3.4
Unconditional bases
90
4
Intermediate operator theory
99
4.1
The spectral radius
99
4.2
Compact linear operators
102
4.3
Fredholm
operators
116
4.4
Finding the essential spectrum
124
vi
Contents
5 Operators
on Hubert space
135
5.1
Bounded operators
135
5.2
Polar decompositions
137
5.3
Orthogonal projections
140
5.4
The spectral theorem
143
5.5
Hilbert-Schmidt operators
151
5.6
Trace class operators
153
5.7
The compactness of f{Q)g{P)
160
6
One-parameter semigroups
163
6.1
Basic properties of semigroups
163
6.2
Other continuity conditions
177
6.3
Some standard examples
182
7
Special classes of semigroup
190
7.1
Norm continuity
190
7.2
Trace class semigroups
194
7.3
Semigroups on dual spaces
197
7.4
Differentiable and analytic vectors
201
7.5
Subordinated semigroups
205
8
Resolvents and generators
210
8.1
Elementary properties of resolvents
210
8.2
Resolvents and semigroups
218
8.3
Classification of generators
227
8.4
Bounded holomorphic semigroups
237
9
Quantitative bounds on operators
245
9.1
Pseudospectra
245
9.2
Generalized spectra and pseudospectra
251
9.3
The numerical range
264
9.4
Higher order hulls and ranges
276
9.5 Von
Neumann's theorem
285
9.6
Peripheral point spectrum
287
10
Quantitative bounds on semigroups
296
10.1
Long time growth bounds
296
10.2
Short time growth bounds
300
10.3
Contractions and dilations
307
10.4
The Cayley transform
310
Contents
vii
10.5
One-parameter groups
315
10.6
Resolvent bounds in Hilbert space
321
11
Perturbation theory
325
11.1
Perturbations of unbounded operators
325
11.2
Relatively compact perturbations
330
11.3
Constant coefficient differential operators on the
half-line
335
11.4
Perturbations: semigroup based methods
339
11.5
Perturbations: resolvent based methods
350
12
Markov chains and graphs
355
12.1
Definition of Markov operators
355
12.2
Irreducibility and spectrum
359
12.3
Continuous time Markov chains
362
12.4
Reversible Markov semigroups
366
12.5
Recurrence and transience
369
12.6
Spectral theory of graphs
374
13
Positive semigroups
380
13.1
Aspects of
positivity
380
13.2
Invariant subsets
386
13.3
Irreducibility
390
13.4
Renormalization
393
13.5
Ergodic theory
395
13.6
Positive semigroups on C(X)
399
14 NSA Schrödinger
operators
408
14.1
Introduction
408
14.2
Bounds on the numerical range
409
14.3
Bounds in one space dimension
412
14.4
The essential spectrum of
Schrödinger
operators
420
14.5
The NSA harmonic oscillator
424
14.6
Semi-classical analysis
427
References
436
Index
446 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T18:03:45Z |
| indexdate | 2024-07-09T20:59:26Z |
| institution | BVB |
| isbn | 9780521866293 |
| language | English |
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| physical | XII, 451 S. graph. Darst. |
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| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Davies, Edward B. 1944- Verfasser (DE-588)137806345 aut Linear operators and their spectra E. Brian Davies 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2007 XII, 451 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 106 Literaturverz. S. 436 - 445 Linear operators Spectral theory (Mathematics) Linearer Operator (DE-588)4167721-3 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Linearer Operator (DE-588)4167721-3 s Spektraltheorie (DE-588)4116561-5 s DE-604 Cambridge studies in advanced mathematics 106 (DE-604)BV000003678 106 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015729141&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Davies, Edward B. 1944- Linear operators and their spectra Cambridge studies in advanced mathematics Linear operators Spectral theory (Mathematics) Linearer Operator (DE-588)4167721-3 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| subject_GND | (DE-588)4167721-3 (DE-588)4116561-5 |
| title | Linear operators and their spectra |
| title_auth | Linear operators and their spectra |
| title_exact_search | Linear operators and their spectra |
| title_exact_search_txtP | Linear operators and their spectra |
| title_full | Linear operators and their spectra E. Brian Davies |
| title_fullStr | Linear operators and their spectra E. Brian Davies |
| title_full_unstemmed | Linear operators and their spectra E. Brian Davies |
| title_short | Linear operators and their spectra |
| title_sort | linear operators and their spectra |
| topic | Linear operators Spectral theory (Mathematics) Linearer Operator (DE-588)4167721-3 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| topic_facet | Linear operators Spectral theory (Mathematics) Linearer Operator Spektraltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015729141&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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