Theory of entire and meromorphic functions: deficient and asymptotic values and singular directions
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Chinese |
| Published: |
Providence, RI
American Mathemat. Soc.
1993
|
| Series: | Translations of mathematical monographs
122 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Chines. übers. |
| Physical Description: | XI, 375 S. |
| ISBN: | 0821845896 |
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MARC
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| 245 | 1 | 0 | |a Theory of entire and meromorphic functions |b deficient and asymptotic values and singular directions |c Zhang Guan-Hou |
| 264 | 1 | |a Providence, RI |b American Mathemat. Soc. |c 1993 | |
| 300 | |a XI, 375 S. | ||
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| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Translations of mathematical monographs |v 122 | |
| 500 | |a Aus d. Chines. übers. | ||
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| 650 | 7 | |a Meromorfe functies |2 gtt | |
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Record in the Search Index
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| adam_text | Contents
Preface ix
Chapter 1. The Nevanlinna Theory 1
§1.1. The Poisson Jensen formula 1
§1.2. The characteristic function 5
§1.3. The Alhfors Shimizu characteristic 7
§1.4. The First Fundamental Theorem 10
§1.5. Lemma on the logarithmic derivative 14
§1.6. The Second Fundamental Theorem 21
§1.7. Annotated notes 33
Chapter 2. The Singular Directions 37
§2.1. On some properties of monotonic functions 37
§2.2. The Boutroux Cartan Theorem 49
§2.3. Fundamental theorem of value distribution of functions
meromorphic in a disk 54
§2.4. The Julia and Borel directions 73
§2.5. On the growth of the entire function 88
§2.6. On the Nevanlinna direction 100
§2.7. Annotated notes 107
Chapter 3. The Deficient Value Theory 109
§3.1. The harmonic measure and the Lindelof type theorem 109
§3.2. The Length Area Principle 118
§3.3. On the growth of meromorphic functions with deficient values 123
§3.4. The Weitsman Theorem 144
§3.5. The Edrei Fuchs Theorem 158
§3.6. Annotated notes 188
Chapter 4. The Asymptotic Value Theory 195
§4.1. The asymptotic value and the transcendental singularity 195
§4.2. The Denjoy Conjecture 208
§4.3. Growth of entire functions along an asymptotic path 232
§4.4. An estimate on the length of the asymptotic path of an enitre
function 247
vii
viii CONTENTS
§4.5. Direct transcendental singularities 257
Chapter 5. The Relationship between Deficient Values and Asymptotic
Values of an Entire Function 271
§5.1. The theorem of the bound and its application regarding
functions meromorphic in the unit disk 271
§5.2. Entire functions of finite lower order 282
§5.3. On entire functions having a finite number of Julia directions 304
§5.4. Extremal length and Ahlfors Distortion Theorem 319
§5.5. On entire functions with zeros distributed on a finite number of
half lines 330
Chapter 6. The Relationship between Deficient Values of a
Meromorphic Function and Direct Transcendental
Singularities of its Inverse Functions 349
§6.1. On meromorphic functions having deficiency sum two 349
§6.2. On meromorphic functions of finite lower order 358
Some Supplementary Results 369
References 371
|
| any_adam_object | 1 |
| author | Zhang, Guan-Hou |
| author_facet | Zhang, Guan-Hou |
| author_role | aut |
| author_sort | Zhang, Guan-Hou |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 750 |
| ctrlnum | (OCoLC)27338143 (DE-599)BVBBV008213619 |
| dewey-full | 515/.98 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.98 |
| dewey-search | 515/.98 |
| dewey-sort | 3515 298 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV008213619 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:16:27Z |
| institution | BVB |
| isbn | 0821845896 |
| language | English Chinese |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005421772 |
| oclc_num | 27338143 |
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| owner | DE-12 DE-11 |
| owner_facet | DE-12 DE-11 |
| physical | XI, 375 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | American Mathemat. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Zhang, Guan-Hou Verfasser aut Zhenghanshu-he-ye chunhanshu-lilun Theory of entire and meromorphic functions deficient and asymptotic values and singular directions Zhang Guan-Hou Providence, RI American Mathemat. Soc. 1993 XI, 375 S. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 122 Aus d. Chines. übers. Fonctions entières Fonctions entières ram Fonctions méromorphes Fonctions méromorphes ram Gehele functies gtt Meromorfe functies gtt Functions, Entire Functions, Meromorphic Ganze Funktion (DE-588)4131592-3 gnd rswk-swf Meromorphe Funktion (DE-588)4136862-9 gnd rswk-swf Ganze Funktion (DE-588)4131592-3 s DE-604 Meromorphe Funktion (DE-588)4136862-9 s Translations of mathematical monographs 122 (DE-604)BV000002394 122 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005421772&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zhang, Guan-Hou Theory of entire and meromorphic functions deficient and asymptotic values and singular directions Translations of mathematical monographs Fonctions entières Fonctions entières ram Fonctions méromorphes Fonctions méromorphes ram Gehele functies gtt Meromorfe functies gtt Functions, Entire Functions, Meromorphic Ganze Funktion (DE-588)4131592-3 gnd Meromorphe Funktion (DE-588)4136862-9 gnd |
| subject_GND | (DE-588)4131592-3 (DE-588)4136862-9 |
| title | Theory of entire and meromorphic functions deficient and asymptotic values and singular directions |
| title_alt | Zhenghanshu-he-ye chunhanshu-lilun |
| title_auth | Theory of entire and meromorphic functions deficient and asymptotic values and singular directions |
| title_exact_search | Theory of entire and meromorphic functions deficient and asymptotic values and singular directions |
| title_full | Theory of entire and meromorphic functions deficient and asymptotic values and singular directions Zhang Guan-Hou |
| title_fullStr | Theory of entire and meromorphic functions deficient and asymptotic values and singular directions Zhang Guan-Hou |
| title_full_unstemmed | Theory of entire and meromorphic functions deficient and asymptotic values and singular directions Zhang Guan-Hou |
| title_short | Theory of entire and meromorphic functions |
| title_sort | theory of entire and meromorphic functions deficient and asymptotic values and singular directions |
| title_sub | deficient and asymptotic values and singular directions |
| topic | Fonctions entières Fonctions entières ram Fonctions méromorphes Fonctions méromorphes ram Gehele functies gtt Meromorfe functies gtt Functions, Entire Functions, Meromorphic Ganze Funktion (DE-588)4131592-3 gnd Meromorphe Funktion (DE-588)4136862-9 gnd |
| topic_facet | Fonctions entières Fonctions méromorphes Gehele functies Meromorfe functies Functions, Entire Functions, Meromorphic Ganze Funktion Meromorphe Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005421772&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
| work_keys_str_mv | AT zhangguanhou zhenghanshuheyechunhanshulilun AT zhangguanhou theoryofentireandmeromorphicfunctionsdeficientandasymptoticvaluesandsingulardirections |