Real and complex analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
McGraw-Hill
2009
|
| Ausgabe: | 3. ed., [Nachdr.] |
| Schriftenreihe: | McGraw-Hill series in higher mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 416 S. |
| ISBN: | 9780070542341 0071002766 0070542341 9780071002769 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV035960504 | ||
| 003 | DE-604 | ||
| 005 | 20100414 | ||
| 007 | t | ||
| 008 | 100119s2009 |||| 00||| eng d | ||
| 020 | |a 9780070542341 |9 978-0-07-054234-1 | ||
| 020 | |a 0071002766 |9 0-07-100276-6 | ||
| 020 | |a 0070542341 |9 0-07-054234-1 | ||
| 020 | |a 9780071002769 |9 978-0-07-100276-9 | ||
| 035 | |a (OCoLC)633155487 | ||
| 035 | |a (DE-599)BVBBV035960504 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-355 |a DE-91G |a DE-19 | ||
| 084 | |a SK 400 |0 (DE-625)143237: |2 rvk | ||
| 084 | |a MAT 260f |2 stub | ||
| 100 | 1 | |a Rudin, Walter |d 1921-2010 |e Verfasser |0 (DE-588)119445670 |4 aut | |
| 245 | 1 | 0 | |a Real and complex analysis |c Walter Rudin |
| 250 | |a 3. ed., [Nachdr.] | ||
| 264 | 1 | |a New York [u.a.] |b McGraw-Hill |c 2009 | |
| 300 | |a XIV, 416 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a McGraw-Hill series in higher mathematics | |
| 650 | 0 | 7 | |a Analysis |0 (DE-588)4001865-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Funktionentheorie |0 (DE-588)4018935-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Reelle Analysis |0 (DE-588)4627581-2 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 689 | 0 | 0 | |a Analysis |0 (DE-588)4001865-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Funktionentheorie |0 (DE-588)4018935-1 |D s |
| 689 | 1 | |8 1\p |5 DE-604 | |
| 689 | 2 | 0 | |a Reelle Analysis |0 (DE-588)4627581-2 |D s |
| 689 | 2 | |8 2\p |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018854678&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-018854678 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804140978411405312 |
|---|---|
| adam_text | CONTENTS
Preface
xiii
Prologue
:
The Exponential Function
ι
Chapter
1
Abstract Integration
5
Set-theoretic notations and terminology
6
The concept of measurability
8
Simple functions
15
Elementary properties of measures
16
Arithmetic in
[0, 00] 18
Integration of positive functions
19
Integration of complex functions
24
The role played by sets of measure zero
27
Exercises
31
Chapter
2
Positive
Borei
Measures
33
Vector spaces
33
Topological preliminaries
35
The Riesz representation theorem
40
Regularity properties of
Borei
measures
47
Lebesgue measure
49
Continuity properties of measurable functions
55
Exercises
57
Chapter
3 ZZ-Spaces
6i
Convex functions and inequalities
61
The IZ-spaces
65
Approximation by continuous functions
69
Exercises 7j
vii
VIU
CONTENTS
Chapter
4
Elementary
Hubert
Space Theory
Inner products and linear functionals
Orthonormal
sets
Trigonometric series
Exercises
76
76
82
88
92
Chapter
5
Examples of Banach Space Techniques
Banach spaces
Consequences of Baire s theorem
Fourier series of continuous functions
Fourier coefficients of
L1
-functions
The Hahn-Banach theorem
An abstract approach to the
Poisson
integral
Exercises
95
95
97
100
103
104
108
112
Chapter
6
Complex Measures
Total variation
Absolute continuity
Consequences of the Radon-Nikodym theorem
Bounded linear functionals on Lp
The Riesz representation theorem
Exercises
116
116
120
124
126
129
132
Chapter
7
Differentiation
Derivatives of measures
The fundamental theorem of Calculus
Differentiable transformations
Exercises
135
135
144
150
156
Chapter
8
Integration on Product Spaces
Measurability on cartesian products
Product measures
The Fubini theorem
Completion of product measures
Convolutions
Distribution functions
Exercises
Chapter
9
Fourier Transforms
Formal properties
The inversion theorem
The Plancherel theorem
The Banach algebra L1
Exercises
160
160
163
164
167
170
172
174
178
178
180
185
190
193
CONTENTS
IX
Chapter
10
Elementary Properties of Holomorphic
Functions
Complex differentiation
Integration over paths
The local Cauchy theorem
The power series representation
The open mapping theorem
The global Cauchy theorem
The calculus of residues
Exercises
196
196
200
204
208
214
217.
224
227
Chapter
11
Harmonic Functions
The Cauchy-Riemann equations
The
Poisson
integral
The mean value property
Boundary behavior of
Poisson
integrals
Representation theorems
Exercises
231
231
233
237
239
245
249
Chapter
12
The Maximum Modulus Principle
Introduction
The
Schwarz
lemma
The
Phragmen-Lindelöf
method
An interpolation theorem
A converse of the maximum modulus theorem
Exercises
253
253
254
256
260
262
264
Chapter
13
Approximation by Rational Functions
Preparation
Runge s theorem
The Mittag-Leffler theorem
Simply connected regions
Exercises
266
266
270
273
274
276
Chapter
14
Conformai
Mapping
Preservation of angles
Linear fractional transformations
Normal families
The Riemann mapping theorem
The class
У
Continuity at the boundary
Conformai
mapping of an annuius
Exercises
278
278
279
281
282
285
289
291
293
X
CONTENTS
Chapter
15
Zeros of Holomorphic Functions
Infinite products
The
Weierstrass
factorization theorem
An interpolation problem
Jensen s formula
Blaschke products
The
Müntz-Szasz
theorem
Exercises
Chapter
16
Analytic Continuation
Regular points and singular points
Continuation along curves
The monodromy theorem
Construction of a modular function
The
Picard
theorem
Exercises
Chapter
17
/P-Spaces
Subharmonic functions
The spaces IP and
N
The theorem of F. and M. Riesz
Factorization theorems
The shift operator
Conjugate functions
Exercises
298
298
301
304
307
310
312
315
319
319
323
326
328
331
332
335
335
337
341
342
346
350
352
Chapter
18
Elementary Theory of Banach Algebras
Introduction
The invertible elements
Ideals and homomorphisms
Applications
Exercises
356
356
357
362
365
369
Chapter
19
Holomorphic Fourier Transforms
Introduction
Two theorems of Paley and Wiener
Quasi-analytic classes
The Denjoy-Carleman theorem
Exercises
Chapter
20
Uniform Approximation by Polynomials
Introduction
■
Some lemmas
Mergelyan s theorem
Exercises
371
371
372
377
380
383
386
386
387
390
394
CONTENTS
Xl
Appendix:
Hausdorff s
Maximality
Theorem
395
Notes and Comments
397
Bibliography
405
List of Special Symbols
407
Index
409
|
| any_adam_object | 1 |
| author | Rudin, Walter 1921-2010 |
| author_GND | (DE-588)119445670 |
| author_facet | Rudin, Walter 1921-2010 |
| author_role | aut |
| author_sort | Rudin, Walter 1921-2010 |
| author_variant | w r wr |
| building | Verbundindex |
| bvnumber | BV035960504 |
| classification_rvk | SK 400 |
| classification_tum | MAT 260f |
| ctrlnum | (OCoLC)633155487 (DE-599)BVBBV035960504 |
| discipline | Mathematik |
| edition | 3. ed., [Nachdr.] |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01948nam a2200493 c 4500</leader><controlfield tag="001">BV035960504</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20100414 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">100119s2009 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780070542341</subfield><subfield code="9">978-0-07-054234-1</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0071002766</subfield><subfield code="9">0-07-100276-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0070542341</subfield><subfield code="9">0-07-054234-1</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780071002769</subfield><subfield code="9">978-0-07-100276-9</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)633155487</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV035960504</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-19</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 400</subfield><subfield code="0">(DE-625)143237:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 260f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Rudin, Walter</subfield><subfield code="d">1921-2010</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)119445670</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Real and complex analysis</subfield><subfield code="c">Walter Rudin</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">3. ed., [Nachdr.]</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York [u.a.]</subfield><subfield code="b">McGraw-Hill</subfield><subfield code="c">2009</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIV, 416 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">McGraw-Hill series in higher mathematics</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Analysis</subfield><subfield code="0">(DE-588)4001865-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Funktionentheorie</subfield><subfield code="0">(DE-588)4018935-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Reelle Analysis</subfield><subfield code="0">(DE-588)4627581-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4123623-3</subfield><subfield code="a">Lehrbuch</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Analysis</subfield><subfield code="0">(DE-588)4001865-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Funktionentheorie</subfield><subfield code="0">(DE-588)4018935-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Reelle Analysis</subfield><subfield code="0">(DE-588)4627581-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018854678&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-018854678</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV035960504 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:08:34Z |
| institution | BVB |
| isbn | 9780070542341 0071002766 0070542341 9780071002769 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018854678 |
| oclc_num | 633155487 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-19 DE-BY-UBM |
| owner_facet | DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-19 DE-BY-UBM |
| physical | XIV, 416 S. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | McGraw-Hill |
| record_format | marc |
| series2 | McGraw-Hill series in higher mathematics |
| spelling | Rudin, Walter 1921-2010 Verfasser (DE-588)119445670 aut Real and complex analysis Walter Rudin 3. ed., [Nachdr.] New York [u.a.] McGraw-Hill 2009 XIV, 416 S. txt rdacontent n rdamedia nc rdacarrier McGraw-Hill series in higher mathematics Analysis (DE-588)4001865-9 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Reelle Analysis (DE-588)4627581-2 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Analysis (DE-588)4001865-9 s DE-604 Funktionentheorie (DE-588)4018935-1 s 1\p DE-604 Reelle Analysis (DE-588)4627581-2 s 2\p DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018854678&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Rudin, Walter 1921-2010 Real and complex analysis Analysis (DE-588)4001865-9 gnd Funktionentheorie (DE-588)4018935-1 gnd Reelle Analysis (DE-588)4627581-2 gnd |
| subject_GND | (DE-588)4001865-9 (DE-588)4018935-1 (DE-588)4627581-2 (DE-588)4123623-3 |
| title | Real and complex analysis |
| title_auth | Real and complex analysis |
| title_exact_search | Real and complex analysis |
| title_full | Real and complex analysis Walter Rudin |
| title_fullStr | Real and complex analysis Walter Rudin |
| title_full_unstemmed | Real and complex analysis Walter Rudin |
| title_short | Real and complex analysis |
| title_sort | real and complex analysis |
| topic | Analysis (DE-588)4001865-9 gnd Funktionentheorie (DE-588)4018935-1 gnd Reelle Analysis (DE-588)4627581-2 gnd |
| topic_facet | Analysis Funktionentheorie Reelle Analysis Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018854678&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT rudinwalter realandcomplexanalysis |