Methods of modern mathematical physics: 1 Functional analysis
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York [u.a.]
Acad. Press
2010
|
| Ausgabe: | Rev. and enl. ed., [reprint.] |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021113121&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Umfang: | XV, 400 S. graph. Darst. |
| ISBN: | 0125850506 9780125850506 |
Internformat
MARC
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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., [reprint.] | ||
| 264 | 1 | |a New York [u.a.] |b Acad. Press |c 2010 | |
| 300 | |a XV, 400 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-021113121 | |
Datensatz im Suchindex
| _version_ | 1819362334603214848 |
|---|---|
| adam_text | Contents
Preface
v
Introduction
vii
Contents of Other Volumes
xv
I: PRELIMINARIES
/.
Sets and functions I
2.
Metric and normed linear spaces
3
Appendix
Lim sup
and
lim inf
Ц
3.
The Lebesgue integral
12
4.
Abstract measure theory
19
5.
Two convergence arguments
26
6.
Equicontinuity
28
Notes
31
Problems
32
II: 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
xli CONTENTS
III: BANACH
SPACES
1. 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
117
Problems
119
V: LOCALLY CONVEX SPACES
/.
General properties
124
2.
Fréchet
spaces
131
3.
Functions of rapid decease and the tempered distributions
133
Appendix The
N
-representation for £r and Sr
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
/.
Topologies on bounded operators
182
2.
Adjoints
185
3.
The spectrum
188
4.
Positive operators and the polar decomposition
195
5.
Compact operators
198
6.
The trace class and
Hubert
-Schmidt ideals
206
Notes
213
Problems
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
1.
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
/.
The Fourier transform on 6r(Un) and
& (№*),
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
¡1.2.
Applications of the Riesz lemma
344
111.1.
Basic properties of L spaces
348
IV.
3.
Proof of Tychonoff
s
theorem
351
IV.
4.
The Riesz-Markov theorem for X
= [0,
I
] 353
IV.
5.
Minimization offunctionals
354
V.5. Proofs of some theorems in nonlinear functional analysis
363
VI.
5.
Applications of compact operators
368
V111.7. Monotone convergence for forms
372
VI
11.8.
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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| id | DE-604.BV037198841 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T14:46:27Z |
| institution | BVB |
| isbn | 0125850506 9780125850506 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021113121 |
| oclc_num | 698547084 |
| open_access_boolean | |
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| owner_facet | DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-898 DE-BY-UBR DE-29T DE-706 DE-703 |
| physical | XV, 400 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Acad. Press |
| record_format | marc |
| spellingShingle | Reed, Michael 1942- Simon, Barry 1946- Methods of modern 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 | Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Funktionalanalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021113121&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002367875 |
| work_keys_str_mv | AT reedmichael methodsofmodernmathematicalphysics1 AT simonbarry methodsofmodernmathematicalphysics1 |