Methods of modern mathematical physics: 1 Functional analysis
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Acad. Press
2007
|
| Edition: | Rev. and enl. ed., [reprint.] |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 400 S. graph. Darst. |
| ISBN: | 0125850506 9780125850506 |
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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 2007 | |
| 300 | |a XV, 400 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Record in the Search Index
| _version_ | 1804138630341459968 |
|---|---|
| adam_text | Contents
Preface
v
Introduction
vii
Contents
of Other Volumes
xv
PRELIMINARIES
/.
Sets and functions I
2.
Metric and normed linear spaces
3
Appendix
Lim
sup and
lim inf
1
1
3.
The Lebesgue integral
12
4.
Abstract measure theory
¡9
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
xii 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: TOPOIOGICAL SPACES
/.
General notions
90
2.
Nets and convergence
95
3.
Compactness
97
Appendix The Stone-
Weierstrass
theorem
¡03
4.
Measure theory on compact spaces I M
5.
Weak topologies on Banach spaces
Ш
Appendix Weak and strong measurability I ¡$
Notes I 7
Problems
H?
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
¥
and
ЅЃ
141
4.
Inductive limits: generalized functions and weak solutions of
partial differential equations
145
5.
Fixed point theorems
¡50
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
/.
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
¡0.
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
У
(W)
and
У (К ),
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
ULI.
Basic properties of V spaces
348
IV.
3.
Proof of
Ту
chonoff
s
theorem
351
IV.
4.
The Riesz-Markov theorem for X
= [0,
I]
353
1V.5. Minimization of functional
354
V.5. Proofs of some theorems in nonlinear functional analysis
363
VI.
5.
Applications of compact operators
368
VI
11.7.
Monotone convergence for forms
372
VII
1.8.
More on the Trotter product formula
377
Uses of the maximum principle
382
Notes
385
Problems
387
List of Symbols
393
Index
395
|
| any_adam_object | 1 |
| author | Reed, Michael 1942- Simon, Barry 1946- |
| author_GND | (DE-588)121352889 (DE-588)134200195 |
| author_facet | Reed, Michael 1942- Simon, Barry 1946- |
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| author_sort | Reed, Michael 1942- |
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| building | Verbundindex |
| bvnumber | BV035321525 |
| ctrlnum | (OCoLC)635166649 (DE-599)BVBBV035321525 |
| edition | Rev. and enl. ed., [reprint.] |
| format | Book |
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| id | DE-604.BV035321525 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:31:14Z |
| institution | BVB |
| isbn | 0125850506 9780125850506 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017126098 |
| oclc_num | 635166649 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR |
| owner_facet | DE-355 DE-BY-UBR |
| physical | XV, 400 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Acad. Press |
| record_format | marc |
| spelling | Reed, Michael 1942- Verfasser (DE-588)121352889 aut Methods of modern mathematical physics 1 Functional analysis Michael Reed ; Barry Simon Rev. and enl. ed., [reprint.] New York [u.a.] Acad. Press 2007 XV, 400 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 s DE-604 Simon, Barry 1946- Verfasser (DE-588)134200195 aut (DE-604)BV002367875 1 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017126098&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| 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=017126098&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 |