Homeomorphisms in analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
AMS
1997
|
| Series: | Mathematical surveys and monographs
51 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
Staff View
MARC
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| adam_text | Contents
Preface xi
The one dimensional case xi
Mappings and measures on Kn xii
Fourier series xiii
Part 1. The One Dimensional Case 1
Chapter 1. Subsets of R 3
1.1. Equivalence classes 3
1.2. Lebesgue equivalence of sets 4
1.3. Density topology 5
1.4. The Zahorski classes 10
Chapter 2. Baire Class 1 13
2.1. Characterization 13
2.2. Absolutely measurable functions 15
2.3. Example 19
Chapter 3. Differentiability Classes 21
3.1. Continuous functions of bounded variation 21
3.2. Continuously differentiable functions 27
3.3. The class Cn [0,1] 30
3.4. Remarks 38
Chapter 4. The Derivative Function 41
4.1. Properties of derivatives 41
4.2. Characterization of the derivative 45
4.3. Proof of Maximoff s theorem 47
4.4. Approximate derivatives 53
4.5. Remarks 56
Part 2. Mappings and Measures on En 59
Chapter 5. Bi Lipschitzian Homeomorphisms 61
5.1. Lebesgue measurability 61
5.2. Length of nonparametric curves 63
5.3. Nonparametric area 68
5.4. Invariance under self homeomorphisms 71
5.5. Invariance of approximately continuous functions 72
5.6. Remarks 74
vii
viii CONTENTS
Chapter 6. Approximation by Homeomorphisms 77
6.1. Background 77
6.2. Approximations by homeomorphisms of one to one maps 78
6.3. Extensions of homeomorphisms 80
6.4. Measurable one to one maps 84
Chapter 7. Measures on Kn 89
7.1. Preliminaries 89
7.2. The one variable case 91
7.3. Constructions of deformations 91
7.4. Deformation theorem 96
7.5. Remarks 97
Chapter 8. Blumberg s Theorem 99
8.1. Blumberg s theorem for metric spaces 99
8.2. Non Blumberg Baire spaces 103
8.3. Homeomorphism analogues 104
Part 3. Fourier Series 109
Chapter 9. Improving the Behavior of Fourier Series 111
9.1. Preliminaries 111
9.2. Uniform convergence 117
9.3. Conjugate functions and the Pal Bohr theorem 120
9.4. Absolute convergence 124
Chapter 10. Preservation of Convergence of Fourier Series 131
10.1. Tests for pointwise and uniform convergence 131
10.2. Fourier series of regulated functions 138
10.3. Uniform convergence of Fourier series 149
Chapter 11. Fourier Series of Integrable Functions 159
11.1. Absolutely measurable functions 159
11.2. Convergence of Fourier series after change of variable 164
11.3. Functions of generalized bounded variation 167
11.4. Preservation of the order of magnitude of Fourier coefficients 178
Appendix A. Supplementary Material 187
Sets, Functions and Measures 187
A.I. Baire, Borel and Lebesgue 187
A.2. Lipschitzian functions 189
A.3. Bounded variation 192
Approximate Continuity 195
A.4. Density topology 195
A.5. Approximately continuous maps into metric spaces 197
Hausdorff Measure and Packing 198
A.6. Hausdorff dimension 198
A.7. Hausdorff packing 199
Nonparametric Length and Area 203
A.8. Nonparametric length 203
A.9. Schwarz s example 203
CONTENTS ix
A.10. Lebesgue s lower semicontinuous area 204
A.ll. Distribution derivatives for one real variable 205
Bibliography 207
Index 213
|
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| spelling | Goffman, Casper Verfasser aut Homeomorphisms in analysis Casper Goffman Providence, RI AMS 1997 txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs 51 Analyse mathématique Analyse mathématique ram Homéomorphismes Homéomorphismes ram Homeomorphisms Mathematical analysis Homöomorphismus (DE-588)4352383-3 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Homöomorphismus (DE-588)4352383-3 s Analysis (DE-588)4001865-9 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009068779&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Goffman, Casper Homeomorphisms in analysis Analyse mathématique Analyse mathématique ram Homéomorphismes Homéomorphismes ram Homeomorphisms Mathematical analysis Homöomorphismus (DE-588)4352383-3 gnd Analysis (DE-588)4001865-9 gnd |
| subject_GND | (DE-588)4352383-3 (DE-588)4001865-9 |
| title | Homeomorphisms in analysis |
| title_auth | Homeomorphisms in analysis |
| title_exact_search | Homeomorphisms in analysis |
| title_full | Homeomorphisms in analysis Casper Goffman |
| title_fullStr | Homeomorphisms in analysis Casper Goffman |
| title_full_unstemmed | Homeomorphisms in analysis Casper Goffman |
| title_short | Homeomorphisms in analysis |
| title_sort | homeomorphisms in analysis |
| topic | Analyse mathématique Analyse mathématique ram Homéomorphismes Homéomorphismes ram Homeomorphisms Mathematical analysis Homöomorphismus (DE-588)4352383-3 gnd Analysis (DE-588)4001865-9 gnd |
| topic_facet | Analyse mathématique Homéomorphismes Homeomorphisms Mathematical analysis Homöomorphismus Analysis |
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