Entire Functions of Several Complex Variables:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1986
|
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
282 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | I - Entire functions of several complex variables constitute an important and original chapter in complex analysis. The study is often motivated by certain applications to specific problems in other areas of mathematics: partial differential equations via the Fourier-Laplace transformation and convolution operators, analytic number theory and problems of transcen dence, or approximation theory, just to name a few. What is important for these applications is to find solutions which satisfy certain growth conditions. The specific problem defines inherently a growth scale, and one seeks a solution of the problem which satisfies certain growth conditions on this scale, and sometimes solutions of minimal asymp totic growth or optimal solutions in some sense. For one complex variable the study of solutions with growth conditions forms the core of the classical theory of entire functions and, historically, the relationship between the number of zeros of an entire function f(z) of one complex variable and the growth of If I (or equivalently log If I) was the first example of a systematic study of growth conditions in a general setting. Problems with growth conditions on the solutions demand much more precise information than existence theorems. The correspondence between two scales of growth can be interpreted often as a correspondence between families of bounded sets in certain Frechet spaces. However, for applications it is of utmost importance to develop precise and explicit representations of the solutions |
| Beschreibung: | 1 Online-Ressource (XII, 272 p) |
| ISBN: | 9783642703447 9783642703461 |
| ISSN: | 0072-7830 |
| DOI: | 10.1007/978-3-642-70344-7 |
Internformat
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| 490 | 0 | |a Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |v 282 |x 0072-7830 | |
| 500 | |a I - Entire functions of several complex variables constitute an important and original chapter in complex analysis. The study is often motivated by certain applications to specific problems in other areas of mathematics: partial differential equations via the Fourier-Laplace transformation and convolution operators, analytic number theory and problems of transcen dence, or approximation theory, just to name a few. What is important for these applications is to find solutions which satisfy certain growth conditions. The specific problem defines inherently a growth scale, and one seeks a solution of the problem which satisfies certain growth conditions on this scale, and sometimes solutions of minimal asymp totic growth or optimal solutions in some sense. For one complex variable the study of solutions with growth conditions forms the core of the classical theory of entire functions and, historically, the relationship between the number of zeros of an entire function f(z) of one complex variable and the growth of If I (or equivalently log If I) was the first example of a systematic study of growth conditions in a general setting. Problems with growth conditions on the solutions demand much more precise information than existence theorems. The correspondence between two scales of growth can be interpreted often as a correspondence between families of bounded sets in certain Frechet spaces. However, for applications it is of utmost importance to develop precise and explicit representations of the solutions | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Differential equations, partial | |
| 650 | 4 | |a Several Complex Variables and Analytic Spaces | |
| 650 | 4 | |a Mathematik | |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Lelong, Pierre 1912-2011 |
| author_GND | (DE-588)117714968 |
| author_facet | Lelong, Pierre 1912-2011 |
| author_role | aut |
| author_sort | Lelong, Pierre 1912-2011 |
| author_variant | p l pl |
| building | Verbundindex |
| bvnumber | BV042422952 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1165490441 (DE-599)BVBBV042422952 |
| dewey-full | 515.94 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.94 |
| dewey-search | 515.94 |
| dewey-sort | 3515.94 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-70344-7 |
| format | Electronic eBook |
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| id | DE-604.BV042422952 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642703447 9783642703461 |
| issn | 0072-7830 |
| language | English |
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| physical | 1 Online-Ressource (XII, 272 p) |
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| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series2 | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |
| spelling | Lelong, Pierre 1912-2011 Verfasser (DE-588)117714968 aut Entire Functions of Several Complex Variables by Pierre Lelong, Lawrence Gruman Berlin, Heidelberg Springer Berlin Heidelberg 1986 1 Online-Ressource (XII, 272 p) txt rdacontent c rdamedia cr rdacarrier Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 282 0072-7830 I - Entire functions of several complex variables constitute an important and original chapter in complex analysis. The study is often motivated by certain applications to specific problems in other areas of mathematics: partial differential equations via the Fourier-Laplace transformation and convolution operators, analytic number theory and problems of transcen dence, or approximation theory, just to name a few. What is important for these applications is to find solutions which satisfy certain growth conditions. The specific problem defines inherently a growth scale, and one seeks a solution of the problem which satisfies certain growth conditions on this scale, and sometimes solutions of minimal asymp totic growth or optimal solutions in some sense. For one complex variable the study of solutions with growth conditions forms the core of the classical theory of entire functions and, historically, the relationship between the number of zeros of an entire function f(z) of one complex variable and the growth of If I (or equivalently log If I) was the first example of a systematic study of growth conditions in a general setting. Problems with growth conditions on the solutions demand much more precise information than existence theorems. The correspondence between two scales of growth can be interpreted often as a correspondence between families of bounded sets in certain Frechet spaces. However, for applications it is of utmost importance to develop precise and explicit representations of the solutions Mathematics Differential equations, partial Several Complex Variables and Analytic Spaces Mathematik 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 Funktionentheorie (DE-588)4018935-1 s Mehrere Variable (DE-588)4277015-4 s 1\p DE-604 Mehrere komplexe Variable (DE-588)4169285-8 s 2\p DE-604 Gruman, Lawrence Sonstige oth https://doi.org/10.1007/978-3-642-70344-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lelong, Pierre 1912-2011 Entire Functions of Several Complex Variables Mathematics Differential equations, partial Several Complex Variables and Analytic Spaces Mathematik 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 by Pierre Lelong, Lawrence Gruman |
| title_fullStr | Entire Functions of Several Complex Variables by Pierre Lelong, Lawrence Gruman |
| title_full_unstemmed | Entire Functions of Several Complex Variables by Pierre Lelong, Lawrence Gruman |
| title_short | Entire Functions of Several Complex Variables |
| title_sort | entire functions of several complex variables |
| topic | Mathematics Differential equations, partial Several Complex Variables and Analytic Spaces Mathematik 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 | Mathematics Differential equations, partial Several Complex Variables and Analytic Spaces Mathematik Ganze Funktion Mehrere Variable Funktionentheorie Mehrere komplexe Variable |
| url | https://doi.org/10.1007/978-3-642-70344-7 |
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