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Titlebook: Basic Oka Theory in Several Complex Variables; Junjiro Noguchi Textbook 2024 The Editor(s) (if applicable) and The Author(s), under exclus

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樓主
發(fā)表于 2025-3-21 16:12:17 | 只看該作者 |倒序瀏覽 |閱讀模式
期刊全稱Basic Oka Theory in Several Complex Variables
影響因子2023Junjiro Noguchi
視頻videohttp://file.papertrans.cn/193/192614/192614.mp4
發(fā)行地址Serves as a textbook in lecture courses of function theory of several complex variables right after one variable.Is based on Oka’s first coherence theorem and the Joku-Iko Principle.Proves Levi‘s prob
學科分類Universitext
圖書封面Titlebook: Basic Oka Theory in Several Complex Variables;  Junjiro Noguchi Textbook 2024 The Editor(s) (if applicable) and The Author(s), under exclus
影響因子.This book provides a new, comprehensive, and self-contained account of Oka theory as an introduction to function theory of several complex variables, mainly concerned with the Three Big Problems (Approximation, Cousin, Pseudoconvexity) that were solved by Kiyoshi Oka and form the basics of the theory. The purpose of the volume is to serve as a textbook in lecture courses right after complex function theory of one variable. The presentation aims to be readable and enjoyable both for those who are beginners in mathematics and for researchers interested in complex analysis in several variables and complex geometry...The nature of the present book is evinced by its approach following Oka’s unpublished five papers of 1943 with his guiding methodological principle termed the “Joku-Iko Principle”, where historically the Pseudoconvexity Problem (Hartogs, Levi) was first solved in all dimensions, even for unramified Riemann domains as well...The method that is used in the book is elementary and direct, not relying on the cohomology theory of sheaves nor on the .L.2-?-bar method, but yet reaches the core of the theory with the complete proofs...Two proofs for Levi’s Problem are provided: On
Pindex Textbook 2024
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沙發(fā)
發(fā)表于 2025-3-21 21:23:06 | 只看該作者
https://doi.org/10.1007/4-431-28055-3and then prove the coherence of ideal sheaves of complex submanifolds (a special case of Oka’s Second Coherence Theorem). We then prove Cartan’s Merging Lemma, the Oka Syzygy for coherent sheaves, and the Oka Extension of the Joku-Iko Principle, which is the key to Oka Theory.
板凳
發(fā)表于 2025-3-22 02:41:06 | 只看該作者
地板
發(fā)表于 2025-3-22 06:44:10 | 只看該作者
https://doi.org/10.1007/4-431-28055-3the results obtained previously, but the path is yet long. Here, introducing the notion of plurisubharmonic (or pseudoconvex) functions, we formulate the Pseudoconvexity Problems and discuss their relations.
5#
發(fā)表于 2025-3-22 11:45:33 | 只看該作者
6#
發(fā)表于 2025-3-22 16:46:18 | 只看該作者
Basic Oka Theory in Several Complex Variables978-981-97-2056-9Series ISSN 0172-5939 Series E-ISSN 2191-6675
7#
發(fā)表于 2025-3-22 20:37:15 | 只看該作者
8#
發(fā)表于 2025-3-22 23:44:35 | 只看該作者
https://doi.org/10.1007/4-431-28055-3and then prove the coherence of ideal sheaves of complex submanifolds (a special case of Oka’s Second Coherence Theorem). We then prove Cartan’s Merging Lemma, the Oka Syzygy for coherent sheaves, and the Oka Extension of the Joku-Iko Principle, which is the key to Oka Theory.
9#
發(fā)表于 2025-3-23 04:06:18 | 只看該作者
10#
發(fā)表于 2025-3-23 07:45:21 | 只看該作者
https://doi.org/10.1007/978-981-97-2056-9Levi problem; Oka theory; complex variables; Oka’s First Coherence Theorem; pseudcoconvex; Cousin problem
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