Entire functions of several complex variables:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2011
|
| Ausgabe: | softcover repr. of the orig. 1. ed. 1986 |
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften
282 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 270 S. |
Internformat
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 |
| 250 | |a softcover repr. of the orig. 1. ed. 1986 | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2011 | |
| 300 | |a XI, 270 S. | ||
| 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 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 |
| 650 | 0 | 7 | |a Mehrere komplexe Variable |0 (DE-588)4169285-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Ganze Funktion |0 (DE-588)4131592-3 |D s |
| 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 |
| 689 | 2 | 1 | |a Mehrere Variable |0 (DE-588)4277015-4 |D s |
| 689 | 2 | |5 DE-604 | |
| 700 | 1 | |a Gruman, Lawrence |e Verfasser |4 aut | |
| 830 | 0 | |a Grundlehren der mathematischen Wissenschaften |v 282 |w (DE-604)BV000000395 |9 282 | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027625121&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027625121 | ||
Datensatz im Suchindex
| _version_ | 1804152697669025792 |
|---|---|
| adam_text | Table
of
Contents
Chapter
1.
Measures of Growth
................. 1
§ 1.
Preliminaries
....................... 1
§2.
Subharmonic and Plurisubharmonic Functions
........ 2
§3.
Norms on
€
and Order of Growth
............. 5
§4.
Minimal Growth: Liouville s Theorem and Generalizations
... 6
§5.
Entire Functions of Finite Order
...............
б
§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.
Locai
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
С
.......... 63
§3.
Canonical Potentials in R
................. 64
§ 4.
The Canonical Representation of Entire Functions of Finite Order
67
§5.
Solution of the
ô
д
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
§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 Cffl
......... 116
§1.
Representation of an Analytic Variety
Y
in C as F~
х(0)
. . . . 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
У
=F-
40).................... 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~l(a) 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
1.
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
С
.........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
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^{r) and E°
210
§4.
Supplementary Results for Proximate Orders with
ρ
> 1..... 212
§5.
The Case p = l
...................... 217
§ 6.
More on Functions of Order Less than One
.......... 225
§7.
Convolution Operators in
€ ................ 227
Historical Notes
........................ 229
Appendix I. Subharmonic and Plurisubharmonic Functions
..... 230
Appendix II. The Existence of Proximate Orders
.......... 242
Appendix III. Solution of the ¿ -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 |
| author_role | aut aut |
| author_sort | Lelong, Pierre 1912-2011 |
| author_variant | p l pl l g lg |
| building | Verbundindex |
| bvnumber | BV042185978 |
| classification_rvk | SK 780 |
| ctrlnum | (OCoLC)897058683 (DE-599)BVBBV042185978 |
| discipline | Mathematik |
| edition | softcover repr. of the orig. 1. ed. 1986 |
| format | Book |
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| id | DE-604.BV042185978 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:14:50Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027625121 |
| oclc_num | 897058683 |
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| owner | DE-739 DE-703 |
| owner_facet | DE-739 DE-703 |
| physical | XI, 270 S. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Springer |
| 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 softcover repr. of the orig. 1. ed. 1986 Berlin [u.a.] Springer 2011 XI, 270 S. txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften 282 Ganze Funktion (DE-588)4131592-3 gnd rswk-swf Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Mehrere komplexe Variable (DE-588)4169285-8 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 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027625121&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 Variable (DE-588)4277015-4 gnd Funktionentheorie (DE-588)4018935-1 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd |
| subject_GND | (DE-588)4131592-3 (DE-588)4277015-4 (DE-588)4018935-1 (DE-588)4169285-8 |
| 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 |
| title_fullStr | Entire functions of several complex variables |
| title_full_unstemmed | Entire functions of several complex variables |
| 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 Variable (DE-588)4277015-4 gnd Funktionentheorie (DE-588)4018935-1 gnd Mehrere komplexe Variable (DE-588)4169285-8 gnd |
| topic_facet | Ganze Funktion Mehrere Variable Funktionentheorie Mehrere komplexe Variable |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027625121&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 |