Dynamics of linear operators:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2009
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge tracts in mathematics
179 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 337 S. |
| ISBN: | 9780521514965 |
Internformat
MARC
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| 035 | |a (DE-599)BVBBV035828329 | ||
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| 100 | 1 | |a Bayart, Frédéric |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Dynamics of linear operators |c Frédéric Bayart ; Étienne Matheron |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2009 | |
| 300 | |a XIV, 337 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cambridge tracts in mathematics |v 179 | |
| 650 | 4 | |a Linear operators | |
| 650 | 0 | 7 | |a Ergodentheorie |0 (DE-588)4015246-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Linearer Operator |0 (DE-588)4167721-3 |2 gnd |9 rswk-swf |
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| 830 | 0 | |a Cambridge tracts in mathematics |v 179 |w (DE-604)BV000000001 |9 179 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-018686926 | ||
Datensatz im Suchindex
| _version_ | 1804140789259829248 |
|---|---|
| adam_text | Contents
Introduction page
viii
1
Hypercyclic
and supercyclic operators
1
1.1
How to prove that an operator is hypercyclic
2
1.2
Some spectral properties
10
1.3
What does the set of hypercyclic vectors look like?
15
1.4
Three examples
17
1.5
Comments and exercises
26
2
Hypercyclicity every where
31
2.1
Mixing operators
31
2.2
Existence of hypercyclic operators
37
2.3
Operators with prescribed orbits
41
2.4
There are many hypercyclic operators
44
2.5
There are few hypercyclic operators
47
2.6
Linear dynamics is complicated
49
2.7
Sums of hypercyclic operators
50
2.8
Comments and exercises
57
3
Connectedness and nypercyclicity
60
3.1
Connectedness and semigroups
61
3.2
Somewhere dense orbits
69
3.3
Comments and exercises
72
4
Weakly mixing operators
75
4.1
Characterizations of weak mixing
76
4.2
Hypercyclic non-weakly-mixing operators
83
4.3
Comments and exercises
92
5
Ergodic theory and linear dynamics
95
5.1
Gaussian measures and covanance operators
97
5.2
Ergodic Gaussian measures for an operator
107
vi
Contents
5.3
How to find an ergodic measure 111
5.4
The results
117
5.5
Examples
120
5.6
Further results
124
5.7
Comments and exercises
129
6
Beyond hypercyclicity
134
6.1
Operators with d-dense orbits
134
6.2
Chaotic operators
137
6.3
Frequently hypercyclic operators
141
6.4
Spaces without chaotic or frequently hypercyclic operators
150
6.5
Almost closing the circle
153
6.6
Comments and exercises
161
7
Common hypercyclic vectors
164
7.1
Common hypercyclic vectors and transitivity
166
7.2
Common hypercyclicity criteria
171
7.3
A probabilistic criterion
179
7.4
Paths of weighted shifts
185
7.5
Comments and exercises
192
8
Hypercyclic subspaces
195
8.1
Hypercyclic subspaces via basic sequences
196
8.2
Hypercyclicity in the operator algebra
199
8.3
Hypercyclic subspaces and the essential spectrum
205
8.4
Examples
209
8.5
Algebras of hypercyclic functions
213
8.6
Comments and exercises
217
9
Supercyclicity and the Angle Criterion
218
9.1
The Angle Criterion
218
9.2
About the converse
219
9.3
The Volterra operator
222
9.4
Parabolic composition operators
224
9.5
Comments and exercises
227
10
Linear dynamics and the weak topology
230
10.1
Weakly closed and weakly dense sequences
231
10.2
Weak dynamics of weighted shifts
241
10.3
Unitary operators
253
10.4
Weak sequential hypercyclicity and supercyclicity
259
10.5
Comments and exercises
261
11
Universality of the Riemann
zeta
function
264
11.1
Voronin s theorem and how to prove it
264
11.2
Dirichlet series and the
zeta
function
268
Contents
vii
11.3
The first half of the proof
276
11.4
Some
Hubert
space geometry
278
11.5
Density of Dirichlet polynomials
280
11.6
Unique ergodicity and the
Kronecker
flow
285
11.7
The second half of the proof
288
11.8
Comments and exercises
290
12
An introduction to Read-type operators
292
12.1
The strategy
292
12.2
First step
293
12.3
Second step
297
12.4
Third step
302
12.5
Comments and an exercise
308
Appendices
310
A Complex analysis
310
В
Function spaces
311
С В
anach space theory
314
D
Spectral theory
316
References
321
Notation
331
Author index
333
Subject index
335
|
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| dewey-full | 515.7246 |
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| discipline | Mathematik |
| edition | 1. publ. |
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| id | DE-604.BV035828329 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:05:33Z |
| institution | BVB |
| isbn | 9780521514965 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018686926 |
| oclc_num | 286434053 |
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| physical | XIV, 337 S. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Bayart, Frédéric Verfasser aut Dynamics of linear operators Frédéric Bayart ; Étienne Matheron 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2009 XIV, 337 S. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 179 Linear operators Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Linearer Operator (DE-588)4167721-3 gnd rswk-swf Linearer Operator (DE-588)4167721-3 s Ergodentheorie (DE-588)4015246-7 s DE-604 Matheron, Étienne Verfasser aut Cambridge tracts in mathematics 179 (DE-604)BV000000001 179 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018686926&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bayart, Frédéric Matheron, Étienne Dynamics of linear operators Cambridge tracts in mathematics Linear operators Ergodentheorie (DE-588)4015246-7 gnd Linearer Operator (DE-588)4167721-3 gnd |
| subject_GND | (DE-588)4015246-7 (DE-588)4167721-3 |
| title | Dynamics of linear operators |
| title_auth | Dynamics of linear operators |
| title_exact_search | Dynamics of linear operators |
| title_full | Dynamics of linear operators Frédéric Bayart ; Étienne Matheron |
| title_fullStr | Dynamics of linear operators Frédéric Bayart ; Étienne Matheron |
| title_full_unstemmed | Dynamics of linear operators Frédéric Bayart ; Étienne Matheron |
| title_short | Dynamics of linear operators |
| title_sort | dynamics of linear operators |
| topic | Linear operators Ergodentheorie (DE-588)4015246-7 gnd Linearer Operator (DE-588)4167721-3 gnd |
| topic_facet | Linear operators Ergodentheorie Linearer Operator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018686926&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000001 |
| work_keys_str_mv | AT bayartfrederic dynamicsoflinearoperators AT matheronetienne dynamicsoflinearoperators |