The theory of cluster sets:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Univ. Press
1966
|
| Schriftenreihe: | Cambridge tracts in mathematics and mathematical physics
56 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 190 - 205 |
| Beschreibung: | XI, 211 S. graph. Darst. |
Internformat
MARC
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| 245 | 1 | 0 | |a The theory of cluster sets |c by E. F. Collingwood and A. J. Lohwater |
| 264 | 1 | |a Cambridge |b Univ. Press |c 1966 | |
| 300 | |a XI, 211 S. |b graph. Darst. | ||
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| 490 | 1 | |a Cambridge tracts in mathematics and mathematical physics |v 56 | |
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| 650 | 4 | |a Cluster set theory | |
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Datensatz im Suchindex
| _version_ | 1804119880217133056 |
|---|---|
| adam_text | CONTENTS
Preface page ix
Chapter 1. introduction
1 The cluster set. Definition 1
2 Definition of a partial cluster set 2
3 Illustrations 3
4 Theorems of Weierstrass and Painleve 4
5 Proofs of the theorems of Painleve and Besicovitch 5
The range and the asymptotic set
6 Definitions. Theorems of Picard, Cartwright and
Iversen 7
7 The notion of capacity 9
8 Counter example for non isolated singularities 10
9 Case of thin sets of non isolated singularities 11
10 Historical note and summary 13
Chapter 2. functions analytic in a
CIRCULAR DISC
Theorems of Fatou and F. and M. Riesz
1 Introduction 17
2 Fatou s theorem on radial limits 17
3 Lindelof s theorem and Fatou s theorem for angular
limits 19
4 Theorem of F. and M. Riesz 21
5 Existence theorems on radial limits 22
vi CONTENTS
Blaschke products
6 Product representation of a bounded function page 28
7 Boundary properties of Blaschke products 31
8 Further properties of Blaschke products. A unique¬
ness theorem 35
9 Functions of bounded characteristic and functions
omitting three values 38
10 Proof that Fatou s theorem is best possible 43
Chapter 3. topics in the theory of
CONFORMAL MAPPING
1 Introduction 46
2 Boundary correspondence under conformal mapping
of a Jordan domain 46
3 The Riesz theorem on conformal mapping of a
Jordan domain with a rectifiable boundary. 49
4 Measure of boundary sets under conformal enlarge¬
ment of domain 54
5 Angular limits of univalent functions 56
6 Correspondence of sets of capacity zero under con¬
formal mapping 64
Chapter 4. intrinsic properties of
CLUSTER SETS
1 Global cluster set, range and asymptotic set 66
2 Existence theorems for global cluster sets 68
3 Sets of maximum indetermination. Existence theo¬
rem for an arbitrary function 72
CONTENTS Vii
4 Maximality theorem for a continuous function page 75
5 Maximality theorems for an arbitrary function 78
6 Symmetric maximality theorems on cluster sets of
an arbitrary function 81
7 Bagemihl s theorem on ambiguous points of an
arbitrary function 83
8 Normal functions. More general classes of functions 86
9 Generalizations 88
Chapter 5. clustbb sets of functions
ANALYTIC IN THE UNIT DISC
1 The Iversen Beurling theorem 89
2 Extensions of the Schwarz reflexion principle 94
3 The Gross Iversen theorem on exceptional values.
Generalizations 101
4 Properties of functions of Seidel s class U 107
5 Scope of the foregoing theorems 109
6 One sided cluster set theorems 110
Chapter 6. boundary theory in the large
1 Method of the inverse function 114
2 The set T(f) for bounded functions 120
3 Boundary theorems in the large 122
4 Cluster sets on spiral paths 129
Chapter 7. boundary theory in the small
1 Introduction 133
2 The main theorem in the small 135
Viii CONTENTS
Chapter 8. further boundary properties of
FUNCTIONS MEROMORPHIC IN THE DISC.
CLASSIFICATION OF SINGULARITIES
1 Introduction page 144
2 Functions with angular limits. Theorems of Privalov
and Plessner 145
3 Radial cluster sets and uniqueness theorems 149
4 Classification and distribution of singularities on K 150
5 Meier s analogue of Plessner s Theorem 153
6 A theorem on polynomial approximation 155
7 An existence theorem on curvilinear cluster sets 162
8 Some consequences of the existence theorem 165
Chapter 9. prime ends
1 Introduction 167
2 Definition of a prime end 168
3 Preliminary lemmas 171
4 Correspondence of frontiers under conformal map¬
ping 172
5 Elementary properties of the space of prime ends 173
6 Alternative metrics and generalizations 175
7 Principal and subsidiary points 176
8 The classification of prime ends 180
9 The distribution of the subsets Sv in $ 182
10 A domain having a bi connected set of accessible
points 185
11 The set of asymmetrical prime ends 188
Bibliography 190
Index of symbols 207
Index 209
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T16:33:13Z |
| institution | BVB |
| language | English |
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| physical | XI, 211 S. graph. Darst. |
| publishDate | 1966 |
| publishDateSearch | 1966 |
| publishDateSort | 1966 |
| publisher | Univ. Press |
| record_format | marc |
| series | Cambridge tracts in mathematics and mathematical physics |
| series2 | Cambridge tracts in mathematics and mathematical physics |
| spelling | Collingwood, Edward F. 1900-1970 Verfasser (DE-588)1036381358 aut The theory of cluster sets by E. F. Collingwood and A. J. Lohwater Cambridge Univ. Press 1966 XI, 211 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics and mathematical physics 56 Literaturverz. S. 190 - 205 Clusters (natuurkunde) gtt Cluster set theory Cluster-Analyse (DE-588)4070044-6 gnd rswk-swf Cluster-Analyse (DE-588)4070044-6 s 1\p DE-604 Lohwater, A. J. Verfasser (DE-588)1067910263 aut Cambridge tracts in mathematics and mathematical physics 56 (DE-604)BV001887938 56 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003555697&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 |
| spellingShingle | Collingwood, Edward F. 1900-1970 Lohwater, A. J. The theory of cluster sets Cambridge tracts in mathematics and mathematical physics Clusters (natuurkunde) gtt Cluster set theory Cluster-Analyse (DE-588)4070044-6 gnd |
| subject_GND | (DE-588)4070044-6 |
| title | The theory of cluster sets |
| title_auth | The theory of cluster sets |
| title_exact_search | The theory of cluster sets |
| title_full | The theory of cluster sets by E. F. Collingwood and A. J. Lohwater |
| title_fullStr | The theory of cluster sets by E. F. Collingwood and A. J. Lohwater |
| title_full_unstemmed | The theory of cluster sets by E. F. Collingwood and A. J. Lohwater |
| title_short | The theory of cluster sets |
| title_sort | the theory of cluster sets |
| topic | Clusters (natuurkunde) gtt Cluster set theory Cluster-Analyse (DE-588)4070044-6 gnd |
| topic_facet | Clusters (natuurkunde) Cluster set theory Cluster-Analyse |
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