Value distribution of meromorphic functions:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Providence, R.I.
American Mathematical Society
2008
|
| Schriftenreihe: | Translations of mathematical monographs
236 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and indexes |
| Beschreibung: | XV, 488 S. Ill., graph. Darst. |
| ISBN: | 9780821842652 |
Internformat
MARC
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| 240 | 1 | 0 | |a Raspredelenie značenij meromorfnych funkcij |
| 245 | 1 | 0 | |a Value distribution of meromorphic functions |c Anatoly A. Goldberg ; Iossif V. Ostrovskii. Transl. by Mikhail Ostrovskii |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 2008 | |
| 300 | |a XV, 488 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Translations of mathematical monographs |v 236 | |
| 500 | |a Includes bibliographical references and indexes | ||
| 650 | 4 | |a Functions, Meromorphic | |
| 650 | 0 | 7 | |a Nevanlinna-Theorie |0 (DE-588)4239989-0 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Ostrovskij, Iosif Vladimirovič |e Verfasser |4 aut | |
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Datensatz im Suchindex
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| adam_text | Contents
Preface xi
Preface to the Russian Edition xiii
Chapter 1. Characteristics of the Behavior of a Meromorphic Function and
the First Fundamental Theorem 1
1. Auxiliary results 1
2. The Nevanlinna, Poisson-Jensen, and Shimizu-Ahlfors formulas 6
3. The Carleman and Levin formulas 10
4. The Nevanlinna characteristics. The first fundamental theorem of the
value distribution theory 13
5. The angular Nevanlinna characteristics, Tsuji characteristics, and
related analogs of the first fundamental theorem 23
6. Relations between the characteristics 28
7. Connection between the growth of the modulus of a meromorphic
function and the growth of its characteristic T(r, /) 36
Chapter 2. Meromorphic Functions of Finite Order 43
1. The growth scale for meromorphic functions 43
2. Proximate order 49
3. Infinite products 54
4. Hadamard s and Lindelof s theorems 57
5. Examples 66
Chapter 3. The Second Fundamental Theorem 87
1. Lemma on the logarithmic derivative 87
2. The Nevanlinna second fundamental theorem 95
3. Analogs of the second fundamental theorem for angular Nevanlinna
characteristics and for Tsuji characteristics 104
Chapter 4. Deficient Values 113
1. Exceptional values 113
2. The set of Valiron exceptional values 116
3. Deficiency relation 121
4. The structure of the set of deficient values 122
5. Entire functions with infinitely many deficient values 132
6. Stability of deficiencies 149
Chapter 5. Asymptotic Properties of Meromorphic Functions and Deficiencies 171
1. Asymptotic values 171
2. Non-asymptotic deficient values 180
vii
viii CONTENTS
3. Meromorphic functions of order less than 1/2 201
4. Bounds for the sum of two deficiencies and related problems 218
5. The growth of a meromorphic function with exceptional values 237
6. Meromorphic functions representable by series of simple fractions 251
Chapter 6. Value Distribution with Respect to the Arguments 259
1. Meromorphic functions with separated poles and zeros 259
2. Meromorphic functions with poles and zeros located close to a system
of rays 276
3. Proofs of Theorems 2.3 and 2.7 294
4. Meromorphic functions with poles and zeros in small angles 306
5. Entire functions with derivatives vanishing only near the real axis 317
Chapter 7. Applications of Riemann Surfaces to Value Distribution 331
1. Geometric meaning of deficient and index values 331
2. Quasiconformal mappings 335
3. The Teichimiller theorem 345
4. Riemann surfaces of the class Fq and line complexes 352
5. Statement of the inverse problem of the value distribution theory.
Riemann surfaces with finitely many logarithmic ends 377
6. Almost periodic ends 385
7. Riemann surfaces with finitely many almost periodic ends 403
8. The inverse problem of the value distribution theory 411
Appendix A. On the Magnitude of Type for an Entire Function 429
Notes 439
Chapter 1 439
Chapter 2 439
Chapter 3 441
Chapter 4 441
Chapter 5 442
Chapter 6 446
Chapter 7 449
Appendix B. A Survey of Some Results after 1970
(by A. Eremenko and J. K. Langley) 453
Chapter 1 453
Chapter 2 454
Chapter 3 455
Chapter 4 458
Chapter 5 459
Chapter 6 462
Chapter 7 463
Appendix A 464
Bibliography 467
References Added to the English Edition 475
Author Index 4gl
CONTENTS ix
Subject Index 485
Notation Index 487
|
| adam_txt |
Contents
Preface xi
Preface to the Russian Edition xiii
Chapter 1. Characteristics of the Behavior of a Meromorphic Function and
the First Fundamental Theorem 1
1. Auxiliary results 1
2. The Nevanlinna, Poisson-Jensen, and Shimizu-Ahlfors formulas 6
3. The Carleman and Levin formulas 10
4. The Nevanlinna characteristics. The first fundamental theorem of the
value distribution theory 13
5. The angular Nevanlinna characteristics, Tsuji characteristics, and
related analogs of the first fundamental theorem 23
6. Relations between the characteristics 28
7. Connection between the growth of the modulus of a meromorphic
function and the growth of its characteristic T(r, /) 36
Chapter 2. Meromorphic Functions of Finite Order 43
1. The growth scale for meromorphic functions 43
2. Proximate order 49
3. Infinite products 54
4. Hadamard's and Lindelof's theorems 57
5. Examples 66
Chapter 3. The Second Fundamental Theorem 87
1. Lemma on the logarithmic derivative 87
2. The Nevanlinna second fundamental theorem 95
3. Analogs of the second fundamental theorem for angular Nevanlinna
characteristics and for Tsuji characteristics 104
Chapter 4. Deficient Values 113
1. Exceptional values 113
2. The set of Valiron exceptional values 116
3. Deficiency relation 121
4. The structure of the set of deficient values 122
5. Entire functions with infinitely many deficient values 132
6. Stability of deficiencies 149
Chapter 5. Asymptotic Properties of Meromorphic Functions and Deficiencies 171
1. Asymptotic values 171
2. Non-asymptotic deficient values 180
vii
viii CONTENTS
3. Meromorphic functions of order less than 1/2 201
4. Bounds for the sum of two deficiencies and related problems 218
5. The growth of a meromorphic function with exceptional values 237
6. Meromorphic functions representable by series of simple fractions 251
Chapter 6. Value Distribution with Respect to the Arguments 259
1. Meromorphic functions with separated poles and zeros 259
2. Meromorphic functions with poles and zeros located close to a system
of rays 276
3. Proofs of Theorems 2.3 and 2.7 294
4. Meromorphic functions with poles and zeros in small angles 306
5. Entire functions with derivatives vanishing only near the real axis 317
Chapter 7. Applications of Riemann Surfaces to Value Distribution 331
1. Geometric meaning of deficient and index values 331
2. Quasiconformal mappings 335
3. The Teichimiller theorem 345
4. Riemann surfaces of the class Fq and line complexes 352
5. Statement of the inverse problem of the value distribution theory.
Riemann surfaces with finitely many logarithmic ends 377
6. Almost periodic ends 385
7. Riemann surfaces with finitely many almost periodic ends 403
8. The inverse problem of the value distribution theory 411
Appendix A. On the Magnitude of Type for an Entire Function 429
Notes 439
Chapter 1 439
Chapter 2 439
Chapter 3 441
Chapter 4 441
Chapter 5 442
Chapter 6 446
Chapter 7 449
Appendix B. A Survey of Some Results after 1970
(by A. Eremenko and J. K. Langley) 453
Chapter 1 453
Chapter 2 454
Chapter 3 455
Chapter 4 458
Chapter 5 459
Chapter 6 462
Chapter 7 463
Appendix A 464
Bibliography 467
References Added to the English Edition 475
Author Index 4gl
CONTENTS ix
Subject Index 485
Notation Index 487 |
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| id | DE-604.BV023299372 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:46:01Z |
| indexdate | 2024-07-09T21:15:17Z |
| institution | BVB |
| isbn | 9780821842652 |
| language | English Russian |
| lccn | 2008060001 |
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| physical | XV, 488 S. Ill., graph. Darst. |
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| publisher | American Mathematical Society |
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| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Golʹdberg, Anatolij A. 1930-2008 Verfasser (DE-588)127350950 aut Raspredelenie značenij meromorfnych funkcij Value distribution of meromorphic functions Anatoly A. Goldberg ; Iossif V. Ostrovskii. Transl. by Mikhail Ostrovskii Providence, R.I. American Mathematical Society 2008 XV, 488 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 236 Includes bibliographical references and indexes Functions, Meromorphic Nevanlinna-Theorie (DE-588)4239989-0 gnd rswk-swf Meromorphe Funktion (DE-588)4136862-9 gnd rswk-swf Meromorphe Funktion (DE-588)4136862-9 s DE-604 Nevanlinna-Theorie (DE-588)4239989-0 s Ostrovskij, Iosif Vladimirovič Verfasser aut Translations of mathematical monographs 236 (DE-604)BV000002394 236 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016483852&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Golʹdberg, Anatolij A. 1930-2008 Ostrovskij, Iosif Vladimirovič Value distribution of meromorphic functions Translations of mathematical monographs Functions, Meromorphic Nevanlinna-Theorie (DE-588)4239989-0 gnd Meromorphe Funktion (DE-588)4136862-9 gnd |
| subject_GND | (DE-588)4239989-0 (DE-588)4136862-9 |
| title | Value distribution of meromorphic functions |
| title_alt | Raspredelenie značenij meromorfnych funkcij |
| title_auth | Value distribution of meromorphic functions |
| title_exact_search | Value distribution of meromorphic functions |
| title_exact_search_txtP | Value distribution of meromorphic functions |
| title_full | Value distribution of meromorphic functions Anatoly A. Goldberg ; Iossif V. Ostrovskii. Transl. by Mikhail Ostrovskii |
| title_fullStr | Value distribution of meromorphic functions Anatoly A. Goldberg ; Iossif V. Ostrovskii. Transl. by Mikhail Ostrovskii |
| title_full_unstemmed | Value distribution of meromorphic functions Anatoly A. Goldberg ; Iossif V. Ostrovskii. Transl. by Mikhail Ostrovskii |
| title_short | Value distribution of meromorphic functions |
| title_sort | value distribution of meromorphic functions |
| topic | Functions, Meromorphic Nevanlinna-Theorie (DE-588)4239989-0 gnd Meromorphe Funktion (DE-588)4136862-9 gnd |
| topic_facet | Functions, Meromorphic Nevanlinna-Theorie Meromorphe Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016483852&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
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