Modern real and complex analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
John Wiley & Sons
1995
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| Series: | A Wiley Interscience Publication
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 489 Seiten graph. Darst. |
| ISBN: | 0471107158 |
Staff View
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| 245 | 1 | 0 | |a Modern real and complex analysis |c Bernard R. Gelbaum |
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| adam_text | Contents
REAL ANALYSIS
1 Fundamentals 3
1.1 Introduction 3
1.2 Topology and Continuity 6
1.3 Baire Category Arguments 18
1.4 Homotopy, Simplices, Fixed Points 20
1.5 Appendix 1: Filters 32
1.6 Appendix 2: Uniformity 34
1.7 Miscellaneous Exercises 38
2 Integration 44
2.1 Daniell Lebesgue Stone Integration 44
2.2 Measurability and Measure 55
2.3 The Riesz Representation Theorem 76
2.4 Complex valued Functions 79
2.5 Miscellaneous Exercises 84
3 Functional Analysis 89
3.1 Introduction 89
3.2 The Spaces W, 1 p oo 92
3.3 Basic Banachology 103
3.4 Weak Topologies 111
3.5 Banach Algebras 116
3.6 Hilbert Space 128
3.7 Miscellaneous Exercises 131
ix
x Contents
4 More Measure Theory 137
4.1 Complex Measures 137
4.2 Comparison of Measures 142
4.3 LRN and Functional Analysis 147
4.4 Product Measures 151
4.5 Nonmeasurable Sets 158
4.6 Differentiation 164
4.7 Derivatives 177
4.8 Curves 185
4.9 Appendix: Haar Measure 187
4.10 Miscellaneous Exercises 192
COMPLEX ANALYSIS
5 Locally Holomorphic Functions 203
5.1 Introduction 203
5.2 Power Series 205
5.3 Basic Holomorphy 209
5.4 Singularities 230
5.5 Homotopy, Homology, and Holomorphy 245
5.6 The Riemann Sphere 251
5.7 Contour Integration 254
5.8 Exterior Calculus 257
5.9 Miscellaneous Exercises 265
6 Harmonic Functions 270
6.1 Basic Properties 270
6.2 Functions Harmonic in a Disc 273
6.3 Subharmonic Functions and Dirichlet s Problem 284
6.4 Appendix: Approximate Identities 296
6.5 Miscellaneous Exercises 296
7 Meromorphic and Entire Functions 701
7.1 Approximations and Representations 301
7.2 Infinite Products 313
7.3 Entire Functions 323
7.4 Miscellaneous Exercises 334
Contents xi
8 Conformal Mapping 336
8.1 Riemann s Mapping Theorem 336
8.2 Mobius Transformations 342
8.3 Bergman s Kernel Functions 349
8.4 Groups and Holomorphy 357
8.5 Conformal Mapping and Green s Function 363
8.6 Miscellaneous Exercises 365
9 Defective Functions 369
9.1 Introduction 369
9.2 Bloch s Theorem 371
9.3 The Little Picard Theorem 374
9.4 The Great Picard Theorem 376
9.5 Miscellaneous Exercises 380
10 Riemann Surfaces 381
10.1 Analytic Continuation 381
10.2 Manifolds and Riemann Surfaces 391
10.3 Covering Spaces and Lifts 409
10.4 Riemann Surfaces and Analysis 419
10.5 The Uniformization Theorem 422
10.6 Miscellaneous Exercises 424
11 Convexity and Complex Analysis 431
11.1 Thorin s Theorem 431
11.2 Applications of Thorin s Theorem 434
12 Several Complex Variables 445
12.1 Survey 445
Bibliography 451
Symbol List 455
Glossary/Index 461
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:50:22Z |
| institution | BVB |
| isbn | 0471107158 |
| language | English |
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| physical | XI, 489 Seiten graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | John Wiley & Sons |
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| spelling | Gelbaum, Bernard R. 1922-2005 Verfasser (DE-588)135764076 aut Modern real and complex analysis Bernard R. Gelbaum New York, NY [u.a.] John Wiley & Sons 1995 XI, 489 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier A Wiley Interscience Publication Analyse (wiskunde) gtt Analyse mathématique Analyse mathématique ram Complexe getallen gtt Reële functies gtt Mathematical analysis Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006863558&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gelbaum, Bernard R. 1922-2005 Modern real and complex analysis Analyse (wiskunde) gtt Analyse mathématique Analyse mathématique ram Complexe getallen gtt Reële functies gtt Mathematical analysis Funktionentheorie (DE-588)4018935-1 gnd |
| subject_GND | (DE-588)4018935-1 |
| title | Modern real and complex analysis |
| title_auth | Modern real and complex analysis |
| title_exact_search | Modern real and complex analysis |
| title_full | Modern real and complex analysis Bernard R. Gelbaum |
| title_fullStr | Modern real and complex analysis Bernard R. Gelbaum |
| title_full_unstemmed | Modern real and complex analysis Bernard R. Gelbaum |
| title_short | Modern real and complex analysis |
| title_sort | modern real and complex analysis |
| topic | Analyse (wiskunde) gtt Analyse mathématique Analyse mathématique ram Complexe getallen gtt Reële functies gtt Mathematical analysis Funktionentheorie (DE-588)4018935-1 gnd |
| topic_facet | Analyse (wiskunde) Analyse mathématique Complexe getallen Reële functies Mathematical analysis Funktionentheorie |
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