Functional analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
McGraw-Hill
1991
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | International series in pure and applied mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XV, 424 S. |
| ISBN: | 711113415X 0070542368 9780070619883 0070619883 |
Internformat
MARC
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| 100 | 1 | |a Rudin, Walter |d 1921-2010 |e Verfasser |0 (DE-588)119445670 |4 aut | |
| 245 | 1 | 0 | |a Functional analysis |c Walter Rudin |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b McGraw-Hill |c 1991 | |
| 300 | |a XV, 424 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a International series in pure and applied mathematics | |
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 7 | |a Analyse fonctionnelle |2 ram | |
| 650 | 7 | |a Functionaalanalyse |2 gtt | |
| 650 | 4 | |a Functional analysis | |
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| 689 | 0 | 0 | |a Funktionalanalysis |0 (DE-588)4018916-8 |D s |
| 689 | 0 | |5 DE-604 | |
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Datensatz im Suchindex
| _version_ | 1804118754029731840 |
|---|---|
| adam_text | CONTENTS
Preface
xiii
Parti General
Theory
1
Topological
Vector Spaces
з
Introduction
3
Separation properties
10
Linear mappings
14
Finite-dimensional spaces
16
Metrization
18
Boundedness and continuity
23
Seminonns and local convexity
25
Quotient spaces
30
Examples
33
Exercises
38
2
Completeness
42
Baire category
42
The Banach-Stemhaus theorem
43
The open mapping theorem
47
The closed graph theorem
50
Bilinear mappings
52
Exercises
53
3
Convexity
56
The Hahn-Banach theorems
56
Weak topologies
62
Compact convex sets
68
Vector-valued integration
77
Holomorphic functions
82
Exercises
85
ix
CONTENTS
Duality
in Banach Spaces 92
The normed dual of a normed space
92
Adjoints
97
Compact
operators
103
Exercises
111
Some
Applications
П6
A
continuity theorem
116
Closed subspaces of IP-spaces
117
The range of a vector-valued measure
120
A generalized Stone-
Weierstrass
theorem
121
Two interpolation theorems
124
Kakutani s fixed point theorem
126
Haar
measure on compact groups
128
Uncomplemented subspaces
132
Sums of
Poisson
kernels
138
Two more fixed point theorems
139
Exercises
144
Part II Distributions and Fourier Transforms
6
Test Functions and Distributions
149
Introduction
149
Test function spaces
151
Calculus with distributions
157
Localization
162
Supports of distributions
164
Distributions as derivatives
167
Convolutions
170
Exercises
177
7
Fourier Transforms
182
Basic properties
182
Tempered distributions
189
Paley-Wiener theorems
196
Sobolev s lemma
202
Exercises
204
8
Applications to Differential Equations
210
Fundamental solutions
210
Elliptic equations
215
Exercises
222
CONTENTS
ХІ
Tauberian
Theory
226
Wiener s theorem
226
The prime number theorem
230
The renewal equation
236
Exercises
239
Part III Banach Algebras and Spectral Theory
10
Banach Algebras
245
Introduction
245
Complex homomorphisms
249
Basic properties of spectra
252
Symbolic calculus
258
The group of invertible elements
267
Lomonosov s invariant subspace theorem
269
Exercises
271
11
Commutative Banach Algebras
275
Ideals and homomorphisms
275
Gelfand transforms
280
Involutions
287
Applications to
noncommutative
algebras
292
Positive functionals
296
Exercises
301
12
Bounded Operators on a Hubert Space
зоб
Basic facts
306
Bounded operators
309
A commutativity theorem
315
Resolutions of the identity
316
The spectral theorem
321
Eigenvalues of normal operators
327
Positive operators and square roots
330
The group of invertible operators
333
A characterization of B*-algebras
336
An ergodic theorem
339
Exercises
341
13
Unbounded Operators
347
Introduction
347
Graphs and symmetric operators
351
The Cayley transform
356
Resolutions of the identity
360
The spectral theorem
368
Semigroups of operators
375
Exercises
385
XU CONTENTS
Appendix A Compactness and Continuity
391
Appendix
В
Notes and Comments
397
Bibliography
412
List of Special Symbols
414
Index
417
|
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| classification_tum | MAT 460f |
| ctrlnum | (OCoLC)21163277 (DE-599)BVBBV004634974 |
| dewey-full | 515/.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.7 |
| dewey-search | 515/.7 |
| dewey-sort | 3515 17 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV004634974 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:15:19Z |
| institution | BVB |
| isbn | 711113415X 0070542368 9780070619883 0070619883 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002845267 |
| oclc_num | 21163277 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-29T DE-92 DE-19 DE-BY-UBM DE-824 DE-706 DE-83 DE-739 DE-11 DE-188 |
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| physical | XV, 424 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | McGraw-Hill |
| record_format | marc |
| series2 | International series in pure and applied mathematics |
| spelling | Rudin, Walter 1921-2010 Verfasser (DE-588)119445670 aut Functional analysis Walter Rudin 2. ed. New York [u.a.] McGraw-Hill 1991 XV, 424 S. txt rdacontent n rdamedia nc rdacarrier International series in pure and applied mathematics Hier auch später erschienene, unveränderte Nachdrucke Analyse fonctionnelle ram Functionaalanalyse gtt Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002845267&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rudin, Walter 1921-2010 Functional analysis Analyse fonctionnelle ram Functionaalanalyse gtt Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4018916-8 |
| title | Functional analysis |
| title_auth | Functional analysis |
| title_exact_search | Functional analysis |
| title_full | Functional analysis Walter Rudin |
| title_fullStr | Functional analysis Walter Rudin |
| title_full_unstemmed | Functional analysis Walter Rudin |
| title_short | Functional analysis |
| title_sort | functional analysis |
| topic | Analyse fonctionnelle ram Functionaalanalyse gtt Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Analyse fonctionnelle Functionaalanalyse Functional analysis Funktionalanalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002845267&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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