Families of exponentials: the method of moments in controllability problems for distributed parameter systems
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1995
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | XV, 302 S. |
| ISBN: | 0521452430 |
Staff View
MARC
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| 100 | 1 | |a Avdonin, Sergej A. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Upravljaemost' sistem s raspredelennymi parametrami i semejstva ėksponent |
| 245 | 1 | 0 | |a Families of exponentials |b the method of moments in controllability problems for distributed parameter systems |c Sergei A. Avdonin ; Sergei A. Ivanov |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 1995 | |
| 300 | |a XV, 302 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Aus dem Russ. übers. | ||
| 650 | 7 | |a Commande, théorie de la |2 ram | |
| 650 | 7 | |a Fonctions exponentionnelles |2 ram | |
| 650 | 7 | |a Fourier, analyse de |2 ram | |
| 650 | 7 | |a Systèmes à paramètres répartis |2 ram | |
| 650 | 7 | |a analyse Fourier |2 inriac | |
| 650 | 7 | |a espace Hilbert |2 inriac | |
| 650 | 7 | |a fonction exponentielle |2 inriac | |
| 650 | 7 | |a méthode moment |2 inriac | |
| 650 | 7 | |a système paramètre réparti |2 inriac | |
| 650 | 7 | |a théorie commande |2 inriac | |
| 650 | 4 | |a Control theory | |
| 650 | 4 | |a Distributed parameter systems | |
| 650 | 4 | |a Exponential functions | |
| 650 | 4 | |a Fourier analysis | |
| 650 | 4 | |a Moment problems (Mathematics) | |
| 650 | 0 | 7 | |a Harmonische Analyse |0 (DE-588)4023453-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Momentenmethode |g Mathematik |0 (DE-588)4320678-5 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Ivanov, Sergej A. |e Verfasser |4 aut | |
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Record in the Search Index
| _version_ | 1804125176400445440 |
|---|---|
| adam_text | FAMILIES OF EXPONENTIALS THE METHOD OF MOMENTS IN CONTROLLABILITY
PROBLEMS FOR DISTRIBUTED PARAMETER SYSTEMS SERGEI A. AVDONIN ST.
PETERSBURG STATE UNIVERSITY SERGEI A. IVANOV ST. PETERSBURG STATE
UNIVERSITY CAMBRIDGE UNIVERSITY PRESS CONTENTS ACKNOWLEDGMENTS . PAGE XI
NOTATION XII INTRODUCTION 1 I ELEMENTS OF HILBERT SPACE THEORY 17 1
FAMILIES OF VECTORS AND FAMILIES OF SUBSPACES 17 1.1 ORTHOPROJECTORS AND
ANGLES BETWEEN SUBSPACES 17 1.2 SKEW PROJECTORS 20 1.3 FAMILIES OF
HILBERT SPACE VECTORS 23 1.4 FAMILIES OF SUBSPACES OF HILBERT SPACE 30
1.5 INVARIANCE OF FAMILY PROPERTIES UNDER MAPPINGS 31 1.6 MINIMALITY OF
FAMILIES OF ELEMENTS AND THEIR PROJECTIONS 32 2 ABSTRACT PROBLEM OF
MOMENTS 34 II FAMILIES OF VECTOR-VALUED EXPONENTIALS 39 1 HARDY SPACES
AND OPERATOR FUNCTIONS 39 1.1 HARDY SPACES 39 1.1.1 DEFINITIONS AND
HILBERT STRUCTURE 39 1.1.2 RELATIONSHIP BETWEEN H 2 ( SPACES 40 1.1.3
CALCULATION OF CAUCHY INTEGRALS BY MEANS OF RESIDUES 41 1.1.4 SIMPLE
FRACTIONS 41 1.1.5 PALEY-WIENER THEOREM AND CONNECTIONS BETWEEN SIMPLE
FRACTIONS AND EXPONENTIALS 41 1.1.6 DECOMPOSITION OF THE SPACE L 2 (U)
AND THE RIESZ PROJECTOR 42 VI CONTENTS 1.2 INNER AND OUTER OPERATOR
FUNCTIONS 42 1.2.1 DEFINITION OF INNER FUNCTIONS 42 1.2.2 CLASSIFICATION
OF SCALAR INNER FUNCTIONS 43 1.2.3 FACTORIZATION OF SCALAR INNER
FUNCTIONS 43 1.2.4 CLASSIFICATION OF INNER OPERATOR FUNCTIONS 44 1.2.5
FACTORIZATION OF INNER OPERATOR FUNCTIONS 44 1.2.6 SCALAR OUTER
FUNCTIONS 45 1.2.7 FACTORIZATION OF SCALAR FUNCTIONS 46 1.2.8 OUTER
OPERATOR FUNCTIONS 46 1.2.9 FACTORIZATION OF STRONG FUNCTIONS 47 1.2.10
SEMISIMPLE ZEROS 47 1.2.11 EXISTENCE OF THE BLASCHKE-POTAPOV PRODUCT 47
1.3 NAGY-FOIAS MODEL OPERATOR 48 1.3.1 SUBSPACES K S 48 1.3.2
DEFINITIONS OF MODEL OPERATORS IN D AND C + 49 1.3.3 THE SPECTRUM AND
EIGENFUNCTIONS OF MODEL OPERATORS IN C+ 49 1.3.4 THE SPECTRUM AND
EIGENFUNCTIONS OF MODEL OPERATORS IN D 50 1.3.5 DISCRETE SPECTRUM
SUBSPACES OF MODEL OPERATORS IN C + 51 1.3.6 INVARIANT SUBSPACES OF A
MODEL OPERATOR IN D 51 1.3.7 COUNTABLE SETS IN THE UPPER HALF-PLANE 52
1.3.8 INDICATIONS FOR A SET TO BE CARLESONIAN 52 1.3.9 SEPARABILITY OF
SIMPLE FRACTION FAMILIES 54 1.3.10 MINIMALITY AND THE BLASCHKE CONDITION
55 1.3.11 IF-BASIS PROPERTY OF SIMPLE SCALAR FRACTION FAMILIES 56 1.3.12
IF-BASIS PROPERTY OF SIMPLE FRACTION FAMILIES AND CARLESON CONSTANT 56
1.3.13 CARLESON-NEWMAN CONDITION AND SIMPLE FRACTIONS 56 1.3.14 THE
INEQUALITIES FOR EXPONENTIAL SUMS ON AN INTERVAL 57 1.3.15 PROPERTY OF
FUNCTIONS FROM THE SUBPSACE K^ 58 1.3.16 ISOMORPHISMS TRANSFERRING
EXPONENTIALS INTO EXPONENTIALS 58 1.4 ENTIRE FUNCTIONS 59 1.4.1 ENTIRE
FUNCTIONS OF THE EXPONENTIAL TYPE 59 1.4.2 GROWTH INDICATOR AND
INDICATOR DIAGRAM 59 1.4.3 FUNCTIONS OF THE CARTWRIGHT CLASS 60 CONTENTS
VII 1.4.4 ZEROS OF CARTWRIGHT-CLASS FUNCTIONS 60 1.4.5 SUMMABILITY AND
GROWTH OF FUNCTIONS ON THE REAL AXIS 61 1.4.6 FUNCTIONS OF THE SINE TYPE
61 VECTOR EXPONENTIAL FAMILIES ON THE SEMIAXIS 61 2.1 MINIMALITY 64 2.2
THE BASIS PROPERTY 67 FAMILIES OF VECTOR EXPONENTIALS ON AN INTERVAL 74
3.1 GEOMETRICAL INDICATIONS OF MINIMAL AND BASIS PROPERTIES 74 3.2
MINIMAL VECTOR FAMILIES AND THE GENERATING FUNCTION 80 3.3 HILBERT
OPERATOR AND EXPONENTIAL FAMILIES ON AN INTERVAL 90 3.4 INDICATIONS FOR
HILBERT OPERATOR TO BE BOUNDED 94 MINIMALITY AND THE BASIS PROPERTY OF
SCALAR EXPONENTIAL FAMILIES IN L 2 (0, T) 99 4.1 MINIMALITY 99 4.2 THE
BASIS PROPERTY OF FAMILY {E IXN } 101 4.3 BASIS SUBFAMILIES OF {E A
} 107 4.4 ALGORITHM OF A BASIS SUBFAMILY EXTRACTION 110 4.5 RIESZ
BASES OF ELEMENTS OF THE FORM T S E A 113 4.6 COMPLEMENTATION OF A
BASIS ON SUBINTERVAL UP TO A BASIS ON INTERVAL 114 4.7 ON THE FAMILIES
OF EXPONENTIALS WITH THE IMAGINARY SPECTRUM 115 ADDITIONAL INFORMATION
ABOUT VECTOR EXPONENTIAL THEORY 117 5.1 RELATIONSHIP OF MINIMALITY OF
VECTOR AND SCALAR EXPONENTIAL FAMILIES ON AN INTERVAL 117 5.2
PERTURBATION OF BASIS FAMILIES 120 5.3 EXPONENTIAL BASES IN SOBOLEV
SPACES 129 5.4 RELATIONSHIP BETWEEN MINIMALITY OF EXPONENTIAL FAMILIES
OF PARABOLIC AND HYPERBOLIC TYPES 133 W-LINEAR INDEPENDENCE OF
EXPONENTIAL FAMILIES 136 6.1 DIRICHLET SERIES 137 6.2 PARABOLIC FAMILY
ON AN INTERVAL 138 6.3 HYPERBOLIC FAMILY ON THE SEMIAXIS 139 6.4
HYPERBOLIC FAMILY ON AN INTERVAL 140 6.5 CO-LINEAR INDEPENDENCE IN L 2
(0, T) 141 6.6 EXCESSIVENESS OF THE EXPONENTIAL FAMILY ARISING IN THE
PROBLEM OF CONTROLLING RECTANGULAR MEMBRANE OSCILLATION 142 VIII
CONTENTS HI FOURIER METHOD IN OPERATOR EQUATIONS AND CONTROLLABILITY 146
TYPES 1 EVOLUTION EQUATIONS OF THE FIRST ORDER IN TIME 146 2 EVOLUTION
EQUATIONS OF THE SECOND ORDER IN TIME 154 3 CONTROLLABILITY TYPES AND
THEIR RELATIONSHIP WITH EXPONENTIAL FAMILIES 161 IV CONTROLLABILITY OF
PARABOLIC-TYPE SYSTEMS 173 1 CONTROL WITH SPATIAL SUPPORT IN THE DOMAIN
175 1.1 INFINITE DIMENSIONAL CONTROL 175 1.2 FINITE DIMENSIONAL CONTROL
178 1.3 POINTWISE CONTROL 180 2 BOUNDARY CONTROL 181 2.1 INFINITE
DIMENSIONAL CONTROL 181 2.2 FINITE DIMENSIONAL CONTROL 186 2.3 POINTWISE
CONTROL 187 V CONTROLLABILITY OF HYPERBOLIC-TYPE SYSTEMS 190 1 CONTROL
WITH SPATIAL SUPPORT IN THE DOMAIN 190 1.1 INFINITE DIMENSIONAL CONTROL
190 1.2 FINITE DIMENSIONAL CONTROL 194 1.3 POINTWISE CONTROL 197 2
BOUNDARY CONTROL 205 2.1 INFINITE DIMENSIONAL CONTROL 205 2.2 FINITE
DIMENSIONAL CONTROL 211 2.3 POINTWISE CONTROL 214 VI CONTROL OF
RECTANGULAR MEMBRANE VIBRATIONS 216 1 BOUNDARY CONTROL 216 1.1
REGULARITY OF THE SOLUTION 216 1.2 LACK OF CONTROLLABILITY 221 1.3
ESTIMATE OF THE CARLESON CONSTANT 223 1.4 POINTWISE BOUNDARY CONTROL 226
2 INITIAL AND POINTWISE CONTROL 228 2.1 PRINCIPAL RESULTS 228 2.2
INITIAL CONTROLLABILITY 229 2.3 LACK OF POINTWISE CONTROLLABILITY 232
2.4 CONSTRUCTION OF BASIS SUBFAMILY 233 VII BOUNDARY CONTROL OF STRING
SYSTEMS 238 1 SYSTEM OF CONNECTED HOMOGENEOUS STRINGS CONTROLLED AT THE
ENDS 238 CONTENTS IX 2 SYSTEM OF STRINGS CONNECTED ELASTICALLY AT ONE
POINT 248 3 CONTROL OF MULTICHANNEL ACOUSTIC SYSTEM 264 4
CONTROLLABILITY OF A NONHOMOGENEOUS STRING CONTROLLED AT THE ENDS 283
REFERENCES 290 INDEX - 301
|
| any_adam_object | 1 |
| author | Avdonin, Sergej A. Ivanov, Sergej A. |
| author_facet | Avdonin, Sergej A. Ivanov, Sergej A. |
| author_role | aut aut |
| author_sort | Avdonin, Sergej A. |
| author_variant | s a a sa saa s a i sa sai |
| building | Verbundindex |
| bvnumber | BV010699475 |
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.2433 |
| dewey-search | 515/.2433 |
| dewey-sort | 3515 42433 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV010699475 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:57:24Z |
| institution | BVB |
| isbn | 0521452430 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007141323 |
| oclc_num | 31376324 |
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| owner | DE-12 DE-355 DE-BY-UBR DE-739 DE-703 DE-706 DE-83 |
| owner_facet | DE-12 DE-355 DE-BY-UBR DE-739 DE-703 DE-706 DE-83 |
| physical | XV, 302 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Avdonin, Sergej A. Verfasser aut Upravljaemost' sistem s raspredelennymi parametrami i semejstva ėksponent Families of exponentials the method of moments in controllability problems for distributed parameter systems Sergei A. Avdonin ; Sergei A. Ivanov 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1995 XV, 302 S. txt rdacontent n rdamedia nc rdacarrier Aus dem Russ. übers. Commande, théorie de la ram Fonctions exponentionnelles ram Fourier, analyse de ram Systèmes à paramètres répartis ram analyse Fourier inriac espace Hilbert inriac fonction exponentielle inriac méthode moment inriac système paramètre réparti inriac théorie commande inriac Control theory Distributed parameter systems Exponential functions Fourier analysis Moment problems (Mathematics) Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Momentenmethode Mathematik (DE-588)4320678-5 gnd rswk-swf System mit verteilten Parametern (DE-588)4058803-8 gnd rswk-swf System mit verteilten Parametern (DE-588)4058803-8 s Harmonische Analyse (DE-588)4023453-8 s Momentenmethode Mathematik (DE-588)4320678-5 s DE-604 Ivanov, Sergej A. Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007141323&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Avdonin, Sergej A. Ivanov, Sergej A. Families of exponentials the method of moments in controllability problems for distributed parameter systems Commande, théorie de la ram Fonctions exponentionnelles ram Fourier, analyse de ram Systèmes à paramètres répartis ram analyse Fourier inriac espace Hilbert inriac fonction exponentielle inriac méthode moment inriac système paramètre réparti inriac théorie commande inriac Control theory Distributed parameter systems Exponential functions Fourier analysis Moment problems (Mathematics) Harmonische Analyse (DE-588)4023453-8 gnd Momentenmethode Mathematik (DE-588)4320678-5 gnd System mit verteilten Parametern (DE-588)4058803-8 gnd |
| subject_GND | (DE-588)4023453-8 (DE-588)4320678-5 (DE-588)4058803-8 |
| title | Families of exponentials the method of moments in controllability problems for distributed parameter systems |
| title_alt | Upravljaemost' sistem s raspredelennymi parametrami i semejstva ėksponent |
| title_auth | Families of exponentials the method of moments in controllability problems for distributed parameter systems |
| title_exact_search | Families of exponentials the method of moments in controllability problems for distributed parameter systems |
| title_full | Families of exponentials the method of moments in controllability problems for distributed parameter systems Sergei A. Avdonin ; Sergei A. Ivanov |
| title_fullStr | Families of exponentials the method of moments in controllability problems for distributed parameter systems Sergei A. Avdonin ; Sergei A. Ivanov |
| title_full_unstemmed | Families of exponentials the method of moments in controllability problems for distributed parameter systems Sergei A. Avdonin ; Sergei A. Ivanov |
| title_short | Families of exponentials |
| title_sort | families of exponentials the method of moments in controllability problems for distributed parameter systems |
| title_sub | the method of moments in controllability problems for distributed parameter systems |
| topic | Commande, théorie de la ram Fonctions exponentionnelles ram Fourier, analyse de ram Systèmes à paramètres répartis ram analyse Fourier inriac espace Hilbert inriac fonction exponentielle inriac méthode moment inriac système paramètre réparti inriac théorie commande inriac Control theory Distributed parameter systems Exponential functions Fourier analysis Moment problems (Mathematics) Harmonische Analyse (DE-588)4023453-8 gnd Momentenmethode Mathematik (DE-588)4320678-5 gnd System mit verteilten Parametern (DE-588)4058803-8 gnd |
| topic_facet | Commande, théorie de la Fonctions exponentionnelles Fourier, analyse de Systèmes à paramètres répartis analyse Fourier espace Hilbert fonction exponentielle méthode moment système paramètre réparti théorie commande Control theory Distributed parameter systems Exponential functions Fourier analysis Moment problems (Mathematics) Harmonische Analyse Momentenmethode Mathematik System mit verteilten Parametern |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007141323&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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