Entire functions of several complex variables:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer-Verlag
1986
|
| Series: | Grundlehren der mathematischen Wissenschaften
282 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 270 Seiten |
| ISBN: | 3540152962 0387152962 |
Staff View
MARC
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| 100 | 1 | |a Lelong, Pierre |d 1912-2011 |e Verfasser |0 (DE-588)117714968 |4 aut | |
| 245 | 1 | 0 | |a Entire functions of several complex variables |c Pierre Lelong, Lawrence Gruman |
| 264 | 1 | |a Berlin [u.a.] |b Springer-Verlag |c 1986 | |
| 300 | |a XI, 270 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Grundlehren der mathematischen Wissenschaften |v 282 | |
| 650 | 0 | 7 | |a Ganze Funktion |0 (DE-588)4131592-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mehrere komplexe Variable |0 (DE-588)4169285-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mehrere Variable |0 (DE-588)4277015-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Funktionentheorie |0 (DE-588)4018935-1 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Mehrere komplexe Variable |0 (DE-588)4169285-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Ganze Funktion |0 (DE-588)4131592-3 |D s |
| 689 | 1 | 1 | |a Funktionentheorie |0 (DE-588)4018935-1 |D s |
| 689 | 1 | 2 | |a Mehrere Variable |0 (DE-588)4277015-4 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Ganze Funktion |0 (DE-588)4131592-3 |D s |
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Record in the Search Index
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|---|---|
| adam_text | Table of Contents
Chapter 1. Measures of Growth 1
§1. Preliminaries 1
§2. Subharmonic and Plurisubharmonic Functions 2
§ 3. Norms on C and Order of Growth 5
§4. Minimal Growth: Liouville s Theorem and Generalizations ... 6
§ 5. Entire Functions of Finite Order 8
§6. Proximate Orders 14
§7. Regularizations 18
§ 8. Indicator of Growth Functions 20
§ 9. Exceptional Sets for Growth Conditions 24
Historical Notes 28
Chapter 2. Local Metric Properties of Zero Sets
and Positive Closed Currents 30
§1. Positive Currents 30
§2. Exterior Product 35
§3. Positive Closed Currents 37
§4. Positive Closed Currents of Degree 1 40
§ 5. Analytic Varieties and Currents of Integration 48
Historical Notes 58
Chapter 3. The Relationship Between the Growth
of an Entire Function and the Growth of its Zero Set 59
§1. Positive Closed Currents of Degree 1 Associated
with a Positive Divisor 60
§2. Indicators of Growth of Cousin Data in C 63
§3. Canonical Potentials in IR™ 64
§4. The Canonical Representation of Entire Functions of Finite Order 67
§5. Solution of the cc Equation 73
§6. The Case of a Cousin Data 77
§7. Slowly Increasing Cousin Data: the Genus q = 0;
the Algebraic Case 79
§8. The Case of Integral Order: Extension of a Theorem of Lindelof . 82
X Table of Contents
§9. Trace of a Cousin Data on Complex Lines 86
§ 10. The Case of a Cousin Data of Infinite Order 89
Historical Notes 94
Chapter 4. Functions of Regular Growth 95
§ 1. General Properties of Functions of Regular growth 96
§2. Distribution of the Zeros of Functions of Regular Growth . . . 106
Historical Notes 114
Chapter 5. Holomorphic Mappings from (C to Cm 116
§1. Representation of an Analytic Variety Y in C as F ^O) . . . .117
§2. Local Potentials and the Defect of Plurisubharmonicity 118
§3. Global Potentials 123
§4. Construction of a System F of Entire Functions
such that Y=F~1(0) 126
§5. The Case of Slow Growth 130
§6. The Algebraic Case 133
§7. The Pseudo Algebraic Case 136
§8. Counterexamples to Uniform Upper Bounds 136
§9. An Upper Bound for the Area of F^^ia) for a Holomorphic Map 138
§ 10. Upper and Lower Bounds for the Trace of an Analytic Variety
on Complex Planes 143
Historical Notes 154
Chapter 6. Application of Entire Functions in Number Theory . . . .155
§1. Preliminaries from Number Theory 155
§2. A Schwarz Lemma 160
§3. Statement and Proof of the Main Theorem 162
Historical Notes 165
Chapter 7. The Indicator of Growth Theorem 167
Historical Notes 176
Chapter 8. Analytic Functionals 177
§1. Convex Sets and the Fourier Borel Transform 178
§2. The Projective Indicator 178
§3. The Projective Laplace Transform 183
§4. The Case of M a Complex Submanifold of C 185
§5. The Generalized Laplace Transform and Indicator Function . . .186
§6. Support for Analytic Functionals 188
§7. Unique Supports for Domains in C 191
§8. Unique Convex Supports 195
Historical Notes 200
Table of Contents XI
Chapter 9. Convolution Operators on Linear Spaces
of Entire Functions 201
§1. Linear Topological Spaces of Entire Functions 201
§2. Theorems of Division 207
§3. Applications of Convolution Operators in the Spaces E p(r) and £° 210
§4. Supplementary Results for Proximate Orders with p 1 212
§5. The Case p= 217
§6. More on Functions of Order Less than One 225
§7. Convolution Operators in C 227
Historical Notes 229
Appendix I. Subharmonic and Plurisubharmonic Functions 230
Appendix II. The Existence of Proximate Orders 242
Appendix III. Solution of the r Equation with Growth Conditions . . 245
Bibliography 254
Index 269
|
| any_adam_object | 1 |
| author | Lelong, Pierre 1912-2011 Gruman, Lawrence |
| author_GND | (DE-588)117714968 |
| author_facet | Lelong, Pierre 1912-2011 Gruman, Lawrence |
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| author_sort | Lelong, Pierre 1912-2011 |
| author_variant | p l pl l g lg |
| building | Verbundindex |
| bvnumber | BV000477665 |
| classification_rvk | SK 780 |
| classification_tum | MAT 305f MAT 320f |
| ctrlnum | (OCoLC)241597874 (DE-599)BVBBV000477665 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000477665 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:14:33Z |
| institution | BVB |
| isbn | 3540152962 0387152962 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000294648 |
| oclc_num | 241597874 |
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| physical | XI, 270 Seiten |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Springer-Verlag |
| record_format | marc |
| series | Grundlehren der mathematischen Wissenschaften |
| series2 | Grundlehren der mathematischen Wissenschaften |
| spelling | Lelong, Pierre 1912-2011 Verfasser (DE-588)117714968 aut Entire functions of several complex variables Pierre Lelong, Lawrence Gruman Berlin [u.a.] Springer-Verlag 1986 XI, 270 Seiten txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften 282 Ganze Funktion (DE-588)4131592-3 gnd rswk-swf Mehrere komplexe Variable (DE-588)4169285-8 gnd rswk-swf Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Ganze Funktion (DE-588)4131592-3 s Mehrere komplexe Variable (DE-588)4169285-8 s DE-604 Funktionentheorie (DE-588)4018935-1 s Mehrere Variable (DE-588)4277015-4 s Gruman, Lawrence Verfasser aut Grundlehren der mathematischen Wissenschaften 282 (DE-604)BV000000395 282 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000294648&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lelong, Pierre 1912-2011 Gruman, Lawrence Entire functions of several complex variables Grundlehren der mathematischen Wissenschaften Ganze Funktion (DE-588)4131592-3 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd Mehrere Variable (DE-588)4277015-4 gnd Funktionentheorie (DE-588)4018935-1 gnd |
| subject_GND | (DE-588)4131592-3 (DE-588)4169285-8 (DE-588)4277015-4 (DE-588)4018935-1 |
| title | Entire functions of several complex variables |
| title_auth | Entire functions of several complex variables |
| title_exact_search | Entire functions of several complex variables |
| title_full | Entire functions of several complex variables Pierre Lelong, Lawrence Gruman |
| title_fullStr | Entire functions of several complex variables Pierre Lelong, Lawrence Gruman |
| title_full_unstemmed | Entire functions of several complex variables Pierre Lelong, Lawrence Gruman |
| title_short | Entire functions of several complex variables |
| title_sort | entire functions of several complex variables |
| topic | Ganze Funktion (DE-588)4131592-3 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd Mehrere Variable (DE-588)4277015-4 gnd Funktionentheorie (DE-588)4018935-1 gnd |
| topic_facet | Ganze Funktion Mehrere komplexe Variable Mehrere Variable Funktionentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000294648&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
| work_keys_str_mv | AT lelongpierre entirefunctionsofseveralcomplexvariables AT grumanlawrence entirefunctionsofseveralcomplexvariables |