Methods of modern mathematical physics: 1 Functional analysis
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Acad. Press
1980
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| Ausgabe: | Rev. and enl. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 400 S. graph. Darst. |
| ISBN: | 0125850506 9780125850506 |
Internformat
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| 245 | 1 | 0 | |a Methods of modern mathematical physics |n 1 |p Functional analysis |c Michael Reed ; Barry Simon |
| 250 | |a Rev. and enl. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Acad. Press |c 1980 | |
| 300 | |a XV, 400 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| adam_text | METHODS OF MODERN MATHEMATICAL PHYSICS I: FUNCTIONAL ANALYSIS REVISED
AND ENLARGED EDITION MICHAEL REED BARRY SIMON DEPARTMENT OF MATHEMATICS
DEPARTMENTS OF MATHEMATICS DUKE UNIVERSITY AND PHYSICS PRINCETON
UNIVERSITY ACADEMIC PRESS A SUBSIDIARY OF HARCOURT BRACE JOVANOVICH,
PUBLISHERS NEW YORK LONDON TORONTO SYDNEY SAN FRANCISCO CONTENTS PREFACE
O V INTRODUCTION VII CONTENTS OF OTHER VOLUMES XV I: PRELIMINARIES /.
SETS AND FUNCTIONS 1 2. METRIC AND NORMED LINEAR SPACES 3 APPENDIX LIM
SUP AND LIM INF 11 3. THE LEBESGUE INTEGRAL 12 4. ABSTRACT MEASURE
THEORY 19 5. TWO CONVERGENCE ARGUMENTS 26 6. EQUICONTINUITY 28 NOTES 31
PROBLEMS 32 HILBERT SPACES /. THE GEOMETRY OF HILBERT SPACE 36 2. THE
RIESZ LEMMA 41 3. ORTHONORMAL BASES 44 4. TENSOR PRODUCTS OF HILBERT
SPACES 49 5. ERGODIC THEORY: AN INTRODUCTION 54 NOTES 60 PROBLEMS 63 XI
XII CONTENTS III: BANACH SPACES /. DEFINITION AND EXAMPLES 67 2. DUALS
AND DOUBLE DUALS 72 3. THE HAHN-BANACH THEOREM 75 4. OPERATIONS ON
BANACH SPACES 78 5. THE BAIRE CATEGORY THEOREM AND ITS CONSEQUENCES 79
NOTES 84 PROBLEMS 86 IV: TOPOLOGICAL SPACES 1 . GENERAL NOTIONS 90 2.
NETS AND CONVERGENCE 95 3. COMPACTNESS 97 APPENDIX THE STONE-WEIERSTRASS
THEOREM 103 4. MEASURE THEORY ON COMPACT SPACES 104 5. WEAK TOPOLOGIES
ON BANACH SPACES - 111 APPENDIX WEAK AND STRONG MEASURABILITY 115 .
NOTES U7 PROBLEMS 119 V: LOCALLY CONVEX SPACES 1. GENERAL PROPERTIES
124 2. FRECHET SPACES 131 3. FUNCTIONS OF RAPID DECEASE AND THE TEMPERED
DISTRIBUTIONS 133 APPENDIX THE N-REPRESENTATION FOR F AND 9 141 4.
INDUCTIVE LIMITS: GENERALIZED FUNCTIONS AND WEAK SOLUTIONS OF PARTIAL
DIFFERENTIAL EQUATIONS 145 5. FIXED POINT THEOREMS 150 6. APPLICATIONS
OF FIXED POINT THEOREMS 153 7. TOPOLOGIES ON LOCALLY CONVEX SPACES:
DUALITY THEORY AND THE STRONG DUAL TOPOLOGY 162 APPENDIX POLARS AND THE
MACKEY*ARENS THEOREM 167 NOTES 169 PROBLEMS 173 CONTENTS XIII VI:
BOUNDED OPERATORS 1. TOPOLOGIES ON BOUNDED OPERATORS 2. ADJOINTS 3. THE
SPECTRUM 4. POSITIVE OPERATORS AND THE POLAR DECOMPOSITION 5. COMPACT
OPERATORS 6. THE TRACE CLASS AND HILBERT-SCHMIDT IDEALS NOTES PROBLEMS X
182 185 188 195 198 206 213 216 VII: THE SPECTRAL THEOREM /. THE
CONTINUOUS FUNCTIONAL CALCULUS 221 2. THE SPECTRAL MEASURES 224 3.
SPECTRAL PROJECTIONS 234 4. ERGODIC THEORY REVISITED: KOOPMANISM 237
NOTES 243 PROBLEMS 245 VIII: UNBOUNDED OPERATORS /. DOMAINS, GRAPHS,
ADJOINTS, AND SPECTRUM 249 2. SYMMETRIC AND SELF-ADJOINT OPERATORS: THE
BASIC CRITERION FOR SELF-ADJOINTNESS 255 3. THE SPECTRAL THEOREM 259 4.
STONE S THEOREM 264 5. FORMAL MANIPULATION IS A TOUCHY BUSINESS:
NELSON S EXAMPLE 270 6. QUADRATIC FORMS 276 7. CONVERGENCE OF UNBOUNDED
OPERATORS 283 8. THE TROTTER PRODUCT FORMULA 295 9. THE POLAR
DECOMPOSITION FOR CLOSED OPERATORS 297 10. TENSOR PRODUCTS 298 11. THREE
MATHEMATICAL PROBLEMS IN QUANTUM MECHANICS 302 NOTES 305 PROBLEMS 312
XIV CONTENTS THE FOURIER TRANSFORM 1. THE FOURIER TRANSFORM ON ^(R )
AND 9 (W), CONVOLUTIONS 318 2. THE RANGE OF THE FOURIER TRANSFORM:
CLASSICAL SPACES 326 3. THE RANGE OF THE FOURIER TRANSFORM: ANALYTICITY
332 NOTES 338 PROBLEMS 339 SUPPLEMENTARY MATERIAL 11.2. APPLICATIONS
OF THE RIESZ LEMMA 344 III.I. BASIC PROPERTIES OF V SPACES 348 IV.3.
PROOF OF TYCHONOFF S THEOREM 351 IV.4. THE RIESZ-MARKOV THEOREM FOR X =
[0, 1] 353 IV.5. MINIMIZATION OF FUNCTIONALS 354 V.5. PROOFS OF SOME
THEOREMS IN NONLINEAR FUNCTIONAL ANALYSIS 363 VI.5. APPLICATIONS OF
COMPACT OPERATORS 368 VIII. 7. MONOTONE CONVERGENCE FOR FORMS 372
VIII.8. MORE ON THE TROTTER PRODUCT FORMULA 377 USES OF THE MAXIMUM
PRINCIPLE 382 NOTES 385 PROBLEMS . 387 LIST OF SYMBOLS 393 INDEX 395
|
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| callnumber-first | Q - Science |
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| classification_tum | MAT 460f PHY 011f |
| ctrlnum | (OCoLC)264141771 (DE-599)BVBBV002367876 |
| dewey-full | 530.1/5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.1/5 |
| dewey-search | 530.1/5 |
| dewey-sort | 3530.1 15 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| edition | Rev. and enl. ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-08-01T16:28:31Z |
| institution | BVB |
| isbn | 0125850506 9780125850506 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001543931 |
| oclc_num | 264141771 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-384 DE-703 DE-824 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-20 DE-862 DE-BY-FWS DE-739 DE-29T DE-92 DE-634 DE-83 DE-188 DE-11 DE-573 |
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| physical | XV, 400 S. graph. Darst. |
| publishDate | 1980 |
| publishDateSearch | 1980 |
| publishDateSort | 1980 |
| publisher | Acad. Press |
| record_format | marc |
| spellingShingle | Reed, Michael 1942- Simon, Barry 1946- Methods of modern mathematical physics Mathematische Physik Mathematical physics Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4018916-8 |
| title | Methods of modern mathematical physics |
| title_auth | Methods of modern mathematical physics |
| title_exact_search | Methods of modern mathematical physics |
| title_full | Methods of modern mathematical physics 1 Functional analysis Michael Reed ; Barry Simon |
| title_fullStr | Methods of modern mathematical physics 1 Functional analysis Michael Reed ; Barry Simon |
| title_full_unstemmed | Methods of modern mathematical physics 1 Functional analysis Michael Reed ; Barry Simon |
| title_short | Methods of modern mathematical physics |
| title_sort | methods of modern mathematical physics functional analysis |
| topic | Mathematische Physik Mathematical physics Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Mathematische Physik Mathematical physics Funktionalanalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001543931&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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Inhaltsverzeichnis
Schweinfurt Magazin
| Signatur: |
2900 06038 |
|---|---|
| Exemplar 1 | ausleihbar Verfügbar Bestellen |