Spectral theory of families of self-adjoint operators:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht u.a.
Kluwer Acad. Publ.
1991
|
| Schriftenreihe: | Mathematics and its applications / Soviet series
57 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus d. Russ. übers. |
| Beschreibung: | XVI, 293 S. |
| ISBN: | 0792307038 |
Internformat
MARC
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| 100 | 1 | |a Samojlenko, Jurij S. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Ėlementy matematičeskoj teorii mnogočastotnych kolebanij invatiantnye tory |
| 245 | 1 | 0 | |a Spectral theory of families of self-adjoint operators |c by Y. S. Samoilenko |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer Acad. Publ. |c 1991 | |
| 300 | |a XVI, 293 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications / Soviet series |v 57 | |
| 500 | |a Aus d. Russ. übers. | ||
| 650 | 0 | 7 | |a Spektraltheorie |0 (DE-588)4116561-5 |2 gnd |9 rswk-swf |
| 655 | 7 | |a Selbstadjugierter Operator |2 gnd |9 rswk-swf | |
| 689 | 0 | 0 | |a Selbstadjugierter Operator |A f |
| 689 | 0 | 1 | |a Spektraltheorie |0 (DE-588)4116561-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 810 | 2 | |a Soviet series |t Mathematics and its applications |v 57 |w (DE-604)BV004708148 |9 57 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002741111&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 940 | 1 | |n oe | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-002741111 | ||
Datensatz im Suchindex
| _version_ | 1804118594021228544 |
|---|---|
| adam_text | CONTENTS
SERIES EDITOR S PREFACE v
PREFACE xi
INTRODUCTION 1
Comments to the introduction 5
PARTI
FAMILIES OF COMMUTING NORMAL OPERATORS
Chapter 1. SPECTRAL ANALYSIS OF COUNTABLE FAMILIES OF COM 7
MUTING SELF ADJOINT OPERATORS (CSO)
1.1 The joint resolution of the identity for a countable family of CSO. 8
Spectral theorem in terms of projection valued measures.
1.2 Thejoint spectrum of a family of CSO. 14
1.3 Countable families of CSO with a simple joint spectrum. 16
1.4 Spectral theorem for a countable collection of CSO in terms of multplica 23
tion operators.
1.5 Unitary invariants of families of CSO. 25
1.6 A joint domain of a family of CSO. Joint analytic, entire and bounded vec 28
tors.
1.7 Functions of a countable family of CSO. Essentially infinite dimensional 35
functions.
1.8 Countable families of CSO connected through linear relations. 38
Comments to Chapter I 40
Chapter 2. UNITARY REPRESENTATIONS OF INDUCTIVE LIMITS OF 41
COMMUTATIVE LOCALLY COMPACT GROUPS
2.1 Inductive limits of locally compact groups. 41
2.2 Character theory. The duality law for inductive limits of commutative 44
locally compact groups.
2.3 Unitary representations of inductive limits of commutative locally compact 46
groups.
2.4 The Spectral theorem for representations in terms of multiplication opera 49
tors.
2.5 Girding domains and entire vectors for a representation. 52
2.6 Unitary representations of K5a. 64
Comments to Chapter 2 65
vii
viii
Chapter 3. DIFFERENTIAL OPERATORS WITH CONSTANT COEFFI 67
CENTS IN SPACES OF FUNCTIONS OF INFINITELY MANY VARI¬
ABLES
3.1 ^ quasi invariant measures on (Bt°° ,B(R°°)). 68
3.2 The countable family (Dt)r=i of CSO. 74
3.3 The Fourier transforms. 78
3.4 Measurable polynomials of (£ t)~=i Differential operators with constant 82
coefficients.
Comments to Chapter 3 85
PART II
INDUCTIVE LIMITS OF FINITE DIMENSIONAL
LIE ALGEBRAS AND THEIR REPRESENTATIONS
Chapter 4. CANONICAL COMMUTATION RELATIONS (CCR) OF SYS 89
TEMS WITH COUNTABLE DEGREES OF FREEDOM
4.1 Canonical commutation relations of systems with finite degrees of freedom. 89
The Stone Von Neumann uniqueness theorem.
4.2 Representations of CCR of systems with countable degrees of freedom. 93
Measures and cocycles.
4.3 Representations with one dimensional cocycle. 96
4.4 Gaussian representations of CCR. 101
4.5 The Garding domain for representations of CCR. 104
Comments to Chapter 4 113
Chapter 5. UNITARY REPRESENTATIONS OF THE GROUP OF FINITE 115
5C/(2) CURRENTS ON A COUNTABLE SET
5.1 Unitary representations of the groups 5£/(2) and SU(2) . 115
5.2 Unitary representations of the group SU(2)%. Measures and cocycles. 116
5.3 Representations with one dimensional cocycle. 121
5.4 SU(2)ni2 and its representations. 122
Comments to Chapter 5 123
Chapter 6. REPRESENTATIONS OF THE GROUP OF UPPER TRIANGU 124
LAR MATRICES
6.1 The groupBo(^v.^) and its completion. B0(JV,K) quasi invariant measures. 124
6.2 Commutative models for representations of the group fl0 W #?)• 128
6.3 Continuous extension of representations of BO(N,1R). 130
6.4 Garding domains for representations of the group BO(N,1R). 132
6.5 Irreducible representations of the group B(N,m). 134
6.6 A class of exact irreducible representations of the group BO(IN, R). 136
ix
6.7 General position representations. 139
6.8 An analogue of the regular representation of the group B0(ffii,nt). 142
Comments to Chapter 6 143
Chapter 7. A CLASS OF INDUCTIVE LIMITS OF GROUPS AND THEIR 145
REPRESENTATIONS
7.1 Groups Go = limG,,G=limG,. 145
—* «—
7.2 Go quasi invariant measures on G. 146
7.3 Irreducible representations of the group G = lim G,. 149
Comments to Chapter 7 150
PART HI
COLLECTIONS OF UNBOUNDED SELF ADJOINT
OPERATORS SATISFYING GENERAL RELATIONS
Chapter 8. ANTICOMMUTING SELF ADJOINT OPERATORS 152
8.1 Anticommuting self adjoint operators. The joint domain. The rigging. 152
8.2 The Spectral theorem for a pair of anticommuting self adjoint operators. 157
8.3 The » algebra and C* algebra of a pair of anticommuting self adjoint opera 159
tors.
8.4 Functions of anticommuting operators. 163
Comments to Chapter 8 164
Chapter 9. FINITE AND COUNTABLE COLLECTIONS OF GRADED 165
COMMUTING SELF ADJOINT OPERATORS (GCSO)
9.1 Finite collections of graded commuting self adjoint operators. 165
9.2 Countable collections of GCSO. The Spectral theorem for tame countable 176
collections of GCSO.
9.3 Representations of the algebra of local observables of a spin system with 180
countable degrees of freedom.
9.4 On dividing countable collections of GCSO into tame and wild . 190
Comments to Chapter 9 191
Chapter 10. COLLECTIONS OF UNBOUNDED CSO (At) and CSO (Bt) SATIS 192
FYING GENERAL COMMUTATION RELATIONS
10.1 Representations of the relation AB=BF(A) using bounded self adjoint 192
operators.
10.2 Representations of the relation AB = BF(A) using unbounded operators. Rig 199
gings and structure theorems.
10.3 Collections A = (Ak) and B = (Bj) satisfying general commutation relations. 206
10.4 Commutative models. 213
Comments to Chapter 10 220
X
PARTIV
REPRESENTATIONS OF OPERATOR ALGEBRAS
AND NON COMMUTATIVE RANDOM SEQUENCES
Chapter 11. C* ALGEBRAS U~ AND THEIR REPRESENTATIONS 222
11.1 C* algebrasoftypeI. 222
11.2 Inductive limits of C* algebras and their representations. 224
11.3 Models for representations of C* algebras. 228
Comments to Chapter 11 230
Chapter 12. NON COMMUTATIVE RANDOM SEQUENCES AND 231
METHODS FOR THEIR CONSTRUCTION
12.1 Non commutative random sequences. 231
12.2 Non commutative moment problem. 233
Comments to Chapter 12 241
BIBLIOGRAPHY 243
INDEX 291
|
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| author | Samojlenko, Jurij S. |
| author_facet | Samojlenko, Jurij S. |
| author_role | aut |
| author_sort | Samojlenko, Jurij S. |
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| bvnumber | BV004417572 |
| classification_rvk | SK 620 |
| classification_tum | MAT 472f |
| ctrlnum | (OCoLC)246570049 (DE-599)BVBBV004417572 |
| discipline | Mathematik |
| format | Book |
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| genre | Selbstadjugierter Operator gnd |
| genre_facet | Selbstadjugierter Operator |
| id | DE-604.BV004417572 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:12:46Z |
| institution | BVB |
| isbn | 0792307038 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002741111 |
| oclc_num | 246570049 |
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| owner_facet | DE-12 DE-91G DE-BY-TUM DE-739 DE-29T DE-703 DE-706 DE-11 |
| physical | XVI, 293 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series2 | Mathematics and its applications / Soviet series |
| spelling | Samojlenko, Jurij S. Verfasser aut Ėlementy matematičeskoj teorii mnogočastotnych kolebanij invatiantnye tory Spectral theory of families of self-adjoint operators by Y. S. Samoilenko Dordrecht u.a. Kluwer Acad. Publ. 1991 XVI, 293 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications / Soviet series 57 Aus d. Russ. übers. Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Selbstadjugierter Operator gnd rswk-swf Selbstadjugierter Operator f Spektraltheorie (DE-588)4116561-5 s DE-604 Soviet series Mathematics and its applications 57 (DE-604)BV004708148 57 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002741111&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Samojlenko, Jurij S. Spectral theory of families of self-adjoint operators Spektraltheorie (DE-588)4116561-5 gnd |
| subject_GND | (DE-588)4116561-5 |
| title | Spectral theory of families of self-adjoint operators |
| title_alt | Ėlementy matematičeskoj teorii mnogočastotnych kolebanij invatiantnye tory |
| title_auth | Spectral theory of families of self-adjoint operators |
| title_exact_search | Spectral theory of families of self-adjoint operators |
| title_full | Spectral theory of families of self-adjoint operators by Y. S. Samoilenko |
| title_fullStr | Spectral theory of families of self-adjoint operators by Y. S. Samoilenko |
| title_full_unstemmed | Spectral theory of families of self-adjoint operators by Y. S. Samoilenko |
| title_short | Spectral theory of families of self-adjoint operators |
| title_sort | spectral theory of families of self adjoint operators |
| topic | Spektraltheorie (DE-588)4116561-5 gnd |
| topic_facet | Spektraltheorie Selbstadjugierter Operator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002741111&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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