Observation and control for operator semigroups:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Basel ; Boston ; Berlin
Birkhäuser
[2009]
|
| Series: | Birkhäuser Advanced Texts
|
| Subjects: | |
| Online Access: | BTU01 TUM01 UBA01 UBM01 UBT01 UER01 UPA01 Volltext Inhaltsverzeichnis |
| Physical Description: | 1 Online-Ressource (xi, 483 Seiten) |
| ISBN: | 9783764389949 |
| DOI: | 10.1007/978-3-7643-8994-9 |
Staff View
MARC
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| 245 | 1 | 0 | |a Observation and control for operator semigroups |c Marius Tucsnak ; George Weiss |
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| 264 | 4 | |c © 2009 | |
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Record in the Search Index
| _version_ | 1804139290072973312 |
|---|---|
| adam_text | CONTENTS
PREFACE
IX
1 OBSERVABILITY AND CONTROLLABILITY FOR FINITE-DIMENSIONAL SYSTEMS
1.1 NORMS AN
D INNER PRODUCT
S 1
1.2 OPERATOR
S ON FINITE-DIMENSIONAL SPACES 5
1.3 MATRI
X EXPONENTIALS 7
1.4 OBSERVABILITY AN
D CONTROLLABILITY FOR FINITE-DIMENSIONAL
LINEAR SYSTEMS 11
1.5 TH
E HAUTU
S TES
T AN
D GRAMIAN
S 15
2 OPERATOR SEMIGROUPS
2.1 STRONGLY CONTINUOUS SEMIGROUPS AND THEI
R GENERATOR
S 20
2.2 TH
E SPECTRU
M AN
D TH
E RESOLVENTS OF A
N OPERATO
R 24
2.3 TH
E RESOLVENTS OF A SEMIGROUP GENERATO
R AN
D
TH
E SPACE D^
00
) 28
2.4 INVARIANT SUBSPACES FOR SEMIGROUPS 33
2.5 RIESZ BASES 36
2.6 DIAGONALIZABLE OPERATOR
S AND SEMIGROUPS 40
2.7 STRONGLY CONTINUOUS GROUPS 47
2.8 TH
E ADJOINT SEMIGROUP 53
2.9 TH
E EMBEDDINGS
V
C
H
C
V
56
2.10 TH
E SPACES
X
X
AN
D X_
X
59
2.11 BOUNDE
D PERTURBATION
S OF A GENERATO
R 65
3 SEMIGROUPS OF CONTRACTIONS
3.1 DISSIPATIVE AN
D M-DISSIPATIVE OPERATOR
S 69
3.2 SELF-ADJOINT OPERATOR
S 73
3.3 POSITIVE OPERATOR
S 78
3.4 TH
E SPACES
HI
AN
D
H_
81
3.5 STURM-LIOUVILL
E OPERATOR
S 88
3.6 TH
E DIRICHLET LAPLACIAN 92
3.7 SKEW-ADJOINT OPERATOR
S 98
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/990501183
DIGITALISIERT DURCH
VI CONTENTS
3.8 TH
E THEOREM
S OF LUMER-PHILLIP
S AN
D STONE 102
3.9 TH
E WAVE EQUATIO
N WIT
H BOUNDAR
Y DAMPIN
G 106
4 CONTROL AND OBSERVATION OPERATORS
4.1 SOLUTIONS OF NON-HOMOGENEOUS EQUATION
S 112
4.2 ADMISSIBLE CONTROL OPERATOR
S 116
4.3 ADMISSIBLE OBSERVATION OPERATOR
S 121
4.4 TH
E DUALIT
Y BETWEEN TH
E ADMISSIBILITY CONCEPTS 126
4.5 TWO REPRESENTATIO
N THEOREM
S 128
4.6 INFINITE-TIME ADMISSIBILITY 134
4.7 REMARK
S AN
D BIBLIOGRAPHICAL NOTE
S ON CHAPTE
R 4 136
5 TESTING ADMISSIBILITY
5.1 GRAMIAN
S AN
D LYAPUNOV INEQUALITIES 139
5.2 ADMISSIBLE CONTROL OPERATOR
S FOR LEFT-INVERTIBLE SEMIGROUPS ...
. 144
5.3 ADMISSIBILITY FOR DIAGONA
L SEMIGROUPS 147
5.4 SOME UNBOUNDE
D PERTURBATION
S OF GENERATOR
S 157
5.5 ADMISSIBLE CONTROL OPERATOR
S FOR PERTURBE
D SEMIGROUPS 164
5.6 REMARK
S AN
D BIBLIOGRAPHICAL NOTE
S ON CHAPTE
R 5 168
6 OBSERVABILITY
6.1 SOME OBSERVABILITY CONCEPTS 173
6.2 SOME EXAMPLES BASED ON TH
E STRIN
G EQUATIO
N 179
6.3 ROBUSTNES
S OF EXACT OBSERVABILITY WIT
H RESPECT T
O ADMISSIBLE
PERTURBATION
S OF TH
E GENERATO
R 184
6.4 SIMULTANEOUS EXACT OBSERVABILITY 190
6.5 A HAUTUS-TYP
E NECESSARY CONDITIO
N FOR EXACT OBSERVABILITY ...
. 194
6.6 HAUTUS-TYP
E TEST
S FOR EXACT OBSERVABILITY WIT
H A SKEW-ADJOINT
GENERATO
R 197
6.7 PROM
W
= -
A$W
T
O
Z = IA^Z
200
6.8 FROM FIRST- T
O SECOND-ORDER EQUATION
S 205
6.9 SPECTRA
L CONDITION
S FOR EXACT OBSERVABILITY WIT
H A
SKEW-ADJOINT GENERATO
R 211
6.10 TH
E CLAMPED EULER-BERNOULL
I BEA
M WIT
H TORQU
E OBSERVATION
A
T A
N ENDPOIN
T 217
6.11 REMARK
S AN
D BIBLIOGRAPHICAL NOTE
S ON CHAPTE
R 6 220
7 OBSERVATION FOR THE WAVE EQUATION
7.1 AN ADMISSIBILITY RESUL
T FOR BOUNDAR
Y OBSERVATIO
N 226
7.2 BOUNDAR
Y EXAC
T OBSERVABILITY 231
7.3 A PERTURBE
D WAVE EQUATIO
N 234
7.4 TH
E WAVE EQUATIO
N WIT
H DISTRIBUTE
D OBSERVATIO
N 240
7.5 SOME CONSEQUENCES FOR TH
E SCHRODINGER AN
D PLAT
E EQUATION
S . . . 247
CONTENTS VII
7.6 TH
E WAVE EQUATION WITH BOUNDAR
Y DAMPIN
G AN
D BOUNDAR
Y
VELOCITY OBSERVATION 251
7.7 REMARK
S AN
D BIBLIOGRAPHICAL NOTES ON CHAPTE
R 7 257
8 NON-HARMONIC FOURIER SERIES AND EXACT OBSERVABILITY
8.1 A THEORE
M OF INGHAM 261
8.2 VARIABLE COEFFICIENTS PDE
S IN ONE SPACE DIMENSION
WIT
H BOUNDAR
Y OBSERVATION 266
8.3 DOMAINS ASSOCIATED WITH A SEQUENCE 270
8.4 TH
E RESULTS OF KAHAN
E AN
D BEURLING 276
8.5 TH
E SCHRODINGER AN
D PLAT
E EQUATIONS IN A RECTANGULA
R DOMAIN
WIT
H DISTRIBUTE
D OBSERVATION 280
8.6 REMARK
S AN
D BIBLIOGRAPHICAL NOTE
S ON CHAPTE
R 8 284
9 OBSERVABILITY FOR PARABOLIC EQUATIONS
9.1 PRELIMINAR
Y RESULTS 287
9.2 FROM
W
=
-A
O
W
T
O
Z
=
~A
O
Z
289
9.3 FINA
L STAT
E OBSERVABILITY WITH GEOMETRIC CONDITIONS 295
9.4 A GLOBAL CARLEMA
N ESTIMAT
E FOR TH
E HEAT OPERATO
R 298
9.5 FINA
L STAT
E OBSERVABILITY WITHOU
T GEOMETRIC CONDITIONS 312
9.6 REMARK
S AN
D BIBLIOGRAPHICAL NOTE
S ON CHAPTE
R 9 314
10 BOUNDARY CONTROL SYSTEMS
10.1 WHA
T IS A BOUNDAR
Y CONTROL SYSTEM? 317
10.2 TWO SIMPLE EXAMPLES IN ONE SPACE DIMENSION 322
10.2.1 A ONE-DIMENSIONAL HEA
T EQUATIO
N WIT
H
NEUMAN
N BOUNDAR
Y CONTROL 323
10.2.2 A STRIN
G EQUATION WIT
H NEUMANN BOUNDAR
Y CONTROL ...
. 324
10.3 A STRIN
G EQUATIO
N WIT
H VARIABLE COEFFICIENTS 326
10.4 AN EULER-BERNOULL
I BEAM WITH TORQU
E CONTROL 330
10.5 AN EULER-BERNOULL
I BEA
M WIT
H ANGULAR VELOCITY CONTROL 334
10.6 TH
E DIRICHLET MA
P ON AN N-DIMENSIONAL DOMAIN 337
10.7 HEAT AN
D SCHRODINGER EQUATIONS WIT
H BOUNDAR
Y CONTROL 341
10.8 TH
E CONVECTION-DIFFUSION EQUATIO
N WIT
H BOUNDAR
Y CONTROL 344
10.9 TH
E WAVE EQUATION WITH DIRICHLET BOUNDAR
Y CONTROL 347
10.10 REMARK
S AN
D BIBLIOGRAPHICAL NOTE
S ON CHAPTE
R 10 352
11 CONTROLLABILITY
11.1 SOME CONTROLLABILITY CONCEPTS 355
11.2 TH
E DUALIT
Y BETWEEN CONTROLLABILITY AN
D OBSERVABILITY 357
11.3 SIMULTANEOUS CONTROLLABILITY AN
D TH
E REACHABLE SPACE
WIT
H
H
1
INPUT
S 364
11.4 AN EXAMPLE OF A COUPLED SYSTEM 371
VIII CONTENTS
11.5 NULL-CONTROLLABILITY FOR HEA
T AN
D CONVECTION-DIFFUSION
EQUATION
S 375
11.6 BOUNDAR
Y CONTROLLABILITY FOR SCHRODINGER AN
D WAVE EQUATION
S . . . 378
11.6.1 BOUNDAR
Y CONTROLLABILITY FOR TH
E SCHRODINGER EQUATIO
N . . 379
11.6.2 BOUNDAR
Y CONTROLLABILITY FOR TH
E WAVE EQUATIO
N 380
11.7 REMARK
S AN
D BIBLIOGRAPHICAL NOTE
S ON CHAPTE
R 11 381
12 APPENDIX I: SOME BACKGROUND ON FUNCTIONAL ANALYSIS
12.1 TH
E CLOSED-GRAPH THEORE
M AN
D SOME CONSEQUENCES 385
12.2 COMPAC
T OPERATOR
S 387
12.3 TH
E SQUAR
E ROO
T OF A POSITIVE OPERATO
R 391
12.4 TH
E FOURIER AN
D LAPLACE TRANSFORMATION
S 394
12.5 BANAC
H SPACE-VALUED
L
P
FUNCTIONS 399
13 APPENDIX II: SOME BACKGROUND ON SOBOLEV SPACES
13.1 TEST FUNCTIONS 404
13.2 DISTRIBUTION
S ON A DOMAIN 408
13.3 TH
E OPERATOR
S DIV, GRAD
, RO
T AN
D A 412
13.4 DEFINITION AN
D FIRST PROPERTIE
S OF SOBOLEV SPACES 415
13.5 REGULARIT
Y OF TH
E BOUNDAR
Y AN
D SOBOLEV SPACES ON MANIFOLDS . . . 420
13.6 TRACE OPERATOR
S AN
D TH
E SPACE WP
O
(N
) 424
13.7 TH
E GREEN FORMULAS AN
D EXTENSIONS OF TRAC
E OPERATOR
S 430
14 APPENDIX III: SOME BACKGROUND ON DIFFERENTIAL CALCULUS
14.1 CRITICA
L POINT
S AN
D SARD
S THEORE
M 435
14.2 EXISTENC
E OF MORSE FUNCTIONS ON
Q.
437
14.3 PROOF OF THEORE
M 9.4.3 441
15 APPENDIX IV: UNIQUE CONTINUATION FOR ELLIPTIC OPERATORS
15.1 A CARLEMA
N ESTIMAT
E FOR ELLIPTIC OPERATOR
S 445
15.2 TH
E UNIQU
E CONTINUATIO
N RESULT
S 454
BIBLIOGRAPHY 459
LIST OF NOTATION 475
INDEX
477
|
| any_adam_object | 1 |
| author | Tucsnak, Marius Weiss, George |
| author_GND | (DE-588)103140693X |
| author_facet | Tucsnak, Marius Weiss, George |
| author_role | aut aut |
| author_sort | Tucsnak, Marius |
| author_variant | m t mt g w gw |
| building | Verbundindex |
| bvnumber | BV035619862 |
| classification_rvk | SK 600 |
| classification_tum | MAT 000 MAT 470 |
| collection | ZDB-2-SMA |
| ctrlnum | (ZDB-2-SMA)978-3-7643-8993-2 (OCoLC)723814691 (DE-599)DNB990501183 |
| dewey-full | 515.724 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.724 |
| dewey-search | 515.724 |
| dewey-sort | 3515.724 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-7643-8994-9 |
| format | Electronic eBook |
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| id | DE-604.BV035619862 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:41:44Z |
| institution | BVB |
| isbn | 9783764389949 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017675036 |
| oclc_num | 723814691 |
| open_access_boolean | |
| owner | DE-634 DE-91 DE-BY-TUM DE-739 DE-703 DE-29 DE-19 DE-BY-UBM DE-384 DE-83 |
| owner_facet | DE-634 DE-91 DE-BY-TUM DE-739 DE-703 DE-29 DE-19 DE-BY-UBM DE-384 DE-83 |
| physical | 1 Online-Ressource (xi, 483 Seiten) |
| psigel | ZDB-2-SMA |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Birkhäuser |
| record_format | marc |
| series2 | Birkhäuser Advanced Texts |
| spelling | Tucsnak, Marius Verfasser (DE-588)103140693X aut Observation and control for operator semigroups Marius Tucsnak ; George Weiss Basel ; Boston ; Berlin Birkhäuser [2009] © 2009 1 Online-Ressource (xi, 483 Seiten) txt rdacontent c rdamedia cr rdacarrier Birkhäuser Advanced Texts Operatorhalbgruppe (DE-588)4172620-0 gnd rswk-swf Unendlichdimensionales System (DE-588)4207956-1 gnd rswk-swf Operatorhalbgruppe (DE-588)4172620-0 s Unendlichdimensionales System (DE-588)4207956-1 s DE-604 Weiss, George Verfasser aut Erscheint auch als Druck-Ausgabe 978-3-7643-8993-2 https://doi.org/10.1007/978-3-7643-8994-9 Verlag URL des Erstveröffentlichers Volltext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017675036&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tucsnak, Marius Weiss, George Observation and control for operator semigroups Operatorhalbgruppe (DE-588)4172620-0 gnd Unendlichdimensionales System (DE-588)4207956-1 gnd |
| subject_GND | (DE-588)4172620-0 (DE-588)4207956-1 |
| title | Observation and control for operator semigroups |
| title_auth | Observation and control for operator semigroups |
| title_exact_search | Observation and control for operator semigroups |
| title_full | Observation and control for operator semigroups Marius Tucsnak ; George Weiss |
| title_fullStr | Observation and control for operator semigroups Marius Tucsnak ; George Weiss |
| title_full_unstemmed | Observation and control for operator semigroups Marius Tucsnak ; George Weiss |
| title_short | Observation and control for operator semigroups |
| title_sort | observation and control for operator semigroups |
| topic | Operatorhalbgruppe (DE-588)4172620-0 gnd Unendlichdimensionales System (DE-588)4207956-1 gnd |
| topic_facet | Operatorhalbgruppe Unendlichdimensionales System |
| url | https://doi.org/10.1007/978-3-7643-8994-9 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017675036&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT tucsnakmarius observationandcontrolforoperatorsemigroups AT weissgeorge observationandcontrolforoperatorsemigroups |