Multivalent functions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge u.a.
Cambridge Univ. Press
1994
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| Ausgabe: | 2. ed. |
| Schriftenreihe: | Cambridge tracts in mathematics
110 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 263 S. |
| ISBN: | 0521460263 |
Internformat
MARC
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| 100 | 1 | |a Hayman, Walter K. |d 1926-2020 |e Verfasser |0 (DE-588)123030889 |4 aut | |
| 245 | 1 | 0 | |a Multivalent functions |c W. K. Hayman |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Cambridge u.a. |b Cambridge Univ. Press |c 1994 | |
| 300 | |a XII, 263 S. | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface page ix
Preface to the second edition xi
1 Elementary bounds for univalent functions 1
1.0 Introduction 1
1.1 Basic results 1
1.2 Elementary growth and distortion theorems 4
1.3 Means and coefficients 9
1.4 Convex univalent functions 11
1.5 Typically real functions 13
1.6 Starlike univalent functions 14
1.7 Asymptotic behaviour of the coefficients 15
2 The growth of finitely mean valent functions 28
2.0 Introduction 28
2.1 A length area principle 29
2.2 The growth of multivalent functions 32
2.3 Some averaging assumptions on p(R) 37
2.4 Simultaneous growth near different boundary points 40
2.5 Applications 42
2.6 Functions of maximal growth 45
2.7 Behaviour near the radius of greatest growth 48
3 Means and coefficients 66
3.0 Introduction 66
3.1 The Hardy Stein Spencer identities 67
3.2 Estimates of the means /^(r) 69
3.3 Estimates for the coefficients 71
3.4 A counter example 76
v
vi Contents
3.5 Coefficients of general mean p valent functions 78
3.6 Growth and omitted values 94
3.7 /c symmetric functions and Szego s conjecture 95
3.8 Power series with gaps 98
4 Symmetrization 103
4.0 Introduction 103
4.1 Lipschitzian functions 104
4.2 The formulae of Gauss and Green 105
4.3 Harmonic functions and the problem of Dirichlet 107
4.4 The Dirichlet integral and capacity 109
4.5 Symmetrization 112
4.6 Symmetrization of functions 116
4.7 Symmetrization of condensers 119
4.8 Green s function and the inner radius 122
4.9 The principle of symmetrization 127
4.10 Applications of Steiner symmetrization 128
4.11 Applications of circular symmetrization 130
4.12 Bounds for |/(z)| and |/ (z)| 133
4.13 Bloch s Theorem 136
4.14 Some other results 140
5 Circumferentially mean p valent functions 144
5.0 Introduction 144
5.1 Functions without zeros 145
5.2 Functions with a zero of order p at the origin 148
5.3 Regularity Theorems: the case a = 0 150
5.4 The case a 0: the minor arc 152
5.5 The major arc 154
5.6 Proof of Theorem 5.5 155
5.7 Applications: the case 1 =1 158
5.8 Functions with /c fold symmetry 159
5.9 Some further results 162
6 Differences of successive coefficients 165
6.0 Introduction 165
6.1 The basic formalism 167
6.2 An application of Green s formula 169
6.3 Estimates for the first term in (6.19) 172
6.4 A 2 point estimate 176
6.5 Statement of the basic theorem 180
Contents vii
6.6 Proof of Theorem 6.2 183
6.7 Coefficient differences of /c symmetric functions 185
6.8 Asymptotic behaviour 186
6.9 Starlike functions 188
6.10 The theorems of Dawei Shen 191
7 The Lowner theory 197
7.0 Introduction 197
7.1 Boundary behaviour in conformal mapping 198
7.2 Transformations 200
7.3 Structure of infinitesimal transformations 203
7.4 The class Si 204
7.5 Continuity properties 207
7.6 The differential equation 209
7.7 Completion of proof of Theorem 7.1 211
7.8 The third coefficient 215
7.9 Coefficients of the inverse functions 222
7.10 The argument of f(z)/z 224
7.11 Radii of convexity and starshapedness 226
7.12 The argument of f(z) 228
7.13 Conclusion 229
8 De Branges Theorem 230
8.0 Introduction 230
8.1 Legendre polynomials 231
8.2 Proof of Milin s conjecture: preliminary results 236
8.3 The Milin Lebedev inequalities 243
8.4 Proof of de Branges Theorem 247
8.5 Some further results 248
Bibliography 255
Index 261
|
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| author | Hayman, Walter K. 1926-2020 |
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| author_facet | Hayman, Walter K. 1926-2020 |
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| dewey-full | 515.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.9 |
| dewey-search | 515.9 |
| dewey-sort | 3515.9 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:45:04Z |
| institution | BVB |
| isbn | 0521460263 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006644152 |
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| physical | XII, 263 S. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Hayman, Walter K. 1926-2020 Verfasser (DE-588)123030889 aut Multivalent functions W. K. Hayman 2. ed. Cambridge u.a. Cambridge Univ. Press 1994 XII, 263 S. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 110 Schlichte Funktion (DE-588)4131418-9 gnd rswk-swf Mehrwertige Funktion (DE-588)4409125-4 gnd rswk-swf Schlichte Funktion (DE-588)4131418-9 s DE-604 Mehrwertige Funktion (DE-588)4409125-4 s Cambridge tracts in mathematics 110 (DE-604)BV000000001 110 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006644152&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hayman, Walter K. 1926-2020 Multivalent functions Cambridge tracts in mathematics Schlichte Funktion (DE-588)4131418-9 gnd Mehrwertige Funktion (DE-588)4409125-4 gnd |
| subject_GND | (DE-588)4131418-9 (DE-588)4409125-4 |
| title | Multivalent functions |
| title_auth | Multivalent functions |
| title_exact_search | Multivalent functions |
| title_full | Multivalent functions W. K. Hayman |
| title_fullStr | Multivalent functions W. K. Hayman |
| title_full_unstemmed | Multivalent functions W. K. Hayman |
| title_short | Multivalent functions |
| title_sort | multivalent functions |
| topic | Schlichte Funktion (DE-588)4131418-9 gnd Mehrwertige Funktion (DE-588)4409125-4 gnd |
| topic_facet | Schlichte Funktion Mehrwertige Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006644152&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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