C0-groups, commutator methods and spectral theory of N-body Hamiltonians
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| Hauptverfasser: | , , |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Basel [u.a.]
Birkhäuser
1996
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| Schriftenreihe: | Progress in mathematics
135 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
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| 245 | 1 | 0 | |a C0-groups, commutator methods and spectral theory of N-body Hamiltonians |c Werner O. Amrein ; Anne Boutet de Monvel ; Vladimir Georgescu |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 1996 | |
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| adam_text | WERNER O. AMREIN ANNE BOUTET DE MONVEL VLADIMIR GEORGESCU CO-GROUPS,
COMMUTATOR METHODS AND SPECTRAL THEORY OF N-BODY HAMILTONIANS BIRKHAUSER
YERLAG BASEL * BOSTON * BERLIN CONTENTS PREFACE IX COMMENTS ON NOTATIONS
XIII CHAPTER 1 SOME SPACES OF FUNCTIONS AND DISTRIBUTIONS 1.1. CALCULUS
ON EUCLIDEAN SPACES 1 1.2. DISTRIBUTIONS, FOURIER TRANSFORMS 5 1.3.
ESTIMATES OF FUNCTIONS AND THEIR FOURIER TRANSFORMS 12 1.4. RAPIDLY
DECREASING DISTRIBUTIONS 24 CHAPTER 2 REAL INTERPOLATION OF BANACH
SPACES 2.1. BANACH SPACES AND LINEAR OPERATORS 29 2.2. THE /^-FUNCTIONAL
36 2.3. THE MEAN AND THE TRACE METHOD 41 2.4. COMPARISON AND DUALITY OF
INTERPOLATION SPACES 46 2.5. THE REITERATION THEOREM 49 2.6.
INTERPOLATION OF OPERATORS 52 2.7. QUASI-LINEARIZABLE COUPLES OF
B-SPACES 54 2.8. FRIEDRICHS COUPLES 59 VI CONTENTS CHAPTER 3 CO-GROUPS
AND FUNCTIONAL CALCULI 3.1. SUBMULTIPLICATIVE FUNCTIONS AND ALGEBRAS
ASSOCIATED TO THEM .... 75 3.2. CO-GROUPS: CONTINUITY PROPERTIES AND
ELEMENTARY FUNCTIONAL CALCULUS 85 3.3. THE DISCRETE SOBOLEV SCALE
ASSOCIATED TO A C 0 -GROUP 94 3.4. BESOV SPACES ASSOCIATED TO A CO-GROUP
122 3.5. LITTLEWOOD-PALEY ESTIMATES 136 3.6. POLYNOMIALLY BOUNDED
CO-GROUPS 148 3.7. CO-GROUPS IN HILBERT SPACES 160 CHAPTER 4 SOME
EXAMPLES OF C O -GROUPS 4.1. WEIGHTED SOBOLEV AND BESOV SPACES 171 4.2.
CO-GROUPS ASSOCIATED TO VECTOR FIELDS 178 CHAPTER 5 AUTOMORPHISMS
ASSOCIATED TO CO-REPRESENTATIONS 5.1. REGULARITY AND COMMUTATORS 193
5.2. REGULARITY OF FRACTIONAL ORDER 199 5.3. REGULARITY PRESERVING AND
REGULARITY IMPROVING OPERATORS 209 5.4. THE SPACES ^ SRIP (R ) 216 5.5.
COMMUTATOR EXPANSIONS 222 5.A. APPENDIX: DIFFERENTIABILITY PROPERTIES OF
OPERATOR-VALUED FUNCTIONS 231 CHAPTER 6 UNITARY REPRESENTATIONS AND
REGULARITY 6.1. REMARKS ON THE FUNCTIONAL CALCULUS FOR SELF-ADJOINT
OPERATORS ... 236 6.2. REGULARITY OF SELF-ADJOINT OPERATORS WITH RESPECT
TO UNITARY CO-GROUPS 242 6.3. UNITARY GROUPS IN FRIEDRICHS COUPLES 253
6.4. ESTIMATES ON (FI(HI) - IP(H 2 ) 260 6.A. APPENDIX: REMARKS ON THE
FUNCTIONAL CALCULUS ASSOCIATED TO 9F IN B(3E) 264 CONTENTS VII CHAPTER 7
THE CONJUGATE OPERATOR METHOD 7.1. LOCALLY SMOOTH OPERATORS AND BOUNDARY
VALUES OF THE RESOLVENT 272 7.2. THE MOURRE ESTIMATE 287 7.3. THE METHOD
OF DIFFERENTIAL INEQUALITIES 299 7.4. SELF-ADJOINT OPERATORS WITH A
SPECTRAL GAP 308 7.5. HAMILTONIANS ASSOCIATED TO SYMMETRIC OPERATORS IN
FRIEDRICHS COUPLES 312 7.6. THE LIMITING ABSORPTION PRINCIPLE FOR SOME
CLASSES OF PSEUDODIFFERENTIAL OPERATORS 330 7.A. APPENDIX: THE GRONWALL
LEMMA 349 7.B. APPENDIX: A COUNTEREXAMPLE. OPTIMALITY OF THE RESULTS ON
THE LIMITING ABSORPTION PRINCIPLE 350 7.C. APPENDIX: ASYMPTOTIC VELOCITY
FOR H = H(P) 355 CHAPTER 8 AN ALGEBRAIC FRAMEWORK FOR THE MANY-BODY
PROBLEM 8.1. SELF-ADJOINT OPERATORS AFFILIATED TO C*-ALGEBRAS 359 8.2.
TENSOR PRODUCTS 372 8.3. ^-FUNCTIONS IN A C*-ALGEBRA SETTING 380 8.4.
GRADED C*-ALGEBRAS 391 CHAPTER 9 SPECTRAL THEORY OF ./V-BODY
HAMILTONIANS 9.1. TENSORIAL FACTORIZATIONS OF &E{X) 401 9.2. SEMICOMPACT
OPERATORS 403 9.3. THE AT-BODY ALGEBRA 409 9.4. NON-RELATIVISTIC A^-BODY
HAMILTONIANS 414 9. A. APPENDIX: REMARKS ON THE G 1 - 1 PROPERTY 430
CHAPTER 10 QUANTUM-MECHANICAL JV-BODY SYSTEMS 10.1. CLUSTERING OF
PARTICLES 433 10.2. QUANTUM-MECHANICAL A^-BODY HAMILTONIANS 439
BIBLIOGRAPHY 445 NOTATIONS 453 INDEX 457
|
| any_adam_object | 1 |
| author | Amrein, Werner O. 1940- Boutet de Monvel, Anne Georgescu, Vladimir |
| author_GND | (DE-588)114043752 |
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| illustrated | Not Illustrated |
| indexdate | 2025-02-03T17:28:01Z |
| institution | BVB |
| isbn | 3764353651 0817653651 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007021379 |
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| physical | XIV, 460 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spellingShingle | Amrein, Werner O. 1940- Boutet de Monvel, Anne Georgescu, Vladimir C0-groups, commutator methods and spectral theory of N-body Hamiltonians Progress in mathematics Opérateur hamiltonien ram Opérateurs auto-adjoints ram Théorie spectrale (Mathématiques) ram Hamiltonian operator Selfadjoint operators Spectral theory (Mathematics) Selbstadjungierter Operator (DE-588)4180810-1 gnd Hamilton-Operator (DE-588)4072278-8 gnd Spektraltheorie (DE-588)4116561-5 gnd Dreikörperproblem (DE-588)4012974-3 gnd Kommutator Quantentheorie (DE-588)4164827-4 gnd |
| subject_GND | (DE-588)4180810-1 (DE-588)4072278-8 (DE-588)4116561-5 (DE-588)4012974-3 (DE-588)4164827-4 |
| title | C0-groups, commutator methods and spectral theory of N-body Hamiltonians |
| title_auth | C0-groups, commutator methods and spectral theory of N-body Hamiltonians |
| title_exact_search | C0-groups, commutator methods and spectral theory of N-body Hamiltonians |
| title_full | C0-groups, commutator methods and spectral theory of N-body Hamiltonians Werner O. Amrein ; Anne Boutet de Monvel ; Vladimir Georgescu |
| title_fullStr | C0-groups, commutator methods and spectral theory of N-body Hamiltonians Werner O. Amrein ; Anne Boutet de Monvel ; Vladimir Georgescu |
| title_full_unstemmed | C0-groups, commutator methods and spectral theory of N-body Hamiltonians Werner O. Amrein ; Anne Boutet de Monvel ; Vladimir Georgescu |
| title_short | C0-groups, commutator methods and spectral theory of N-body Hamiltonians |
| title_sort | c0 groups commutator methods and spectral theory of n body hamiltonians |
| topic | Opérateur hamiltonien ram Opérateurs auto-adjoints ram Théorie spectrale (Mathématiques) ram Hamiltonian operator Selfadjoint operators Spectral theory (Mathematics) Selbstadjungierter Operator (DE-588)4180810-1 gnd Hamilton-Operator (DE-588)4072278-8 gnd Spektraltheorie (DE-588)4116561-5 gnd Dreikörperproblem (DE-588)4012974-3 gnd Kommutator Quantentheorie (DE-588)4164827-4 gnd |
| topic_facet | Opérateur hamiltonien Opérateurs auto-adjoints Théorie spectrale (Mathématiques) Hamiltonian operator Selfadjoint operators Spectral theory (Mathematics) Selbstadjungierter Operator Hamilton-Operator Spektraltheorie Dreikörperproblem Kommutator Quantentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007021379&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
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