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Titlebook: Analytic Function Theory of Several Variables; Elements of Oka’s Co Junjiro Noguchi Textbook 2016 Springer Science+Business Media Singapore

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發(fā)表于 2025-3-21 19:31:45 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
期刊全稱(chēng)Analytic Function Theory of Several Variables
期刊簡(jiǎn)稱(chēng)Elements of Oka’s Co
影響因子2023Junjiro Noguchi
視頻videohttp://file.papertrans.cn/157/156516/156516.mp4
發(fā)行地址Is an easily readable and enjoyable text on the classical analytic function theory of several complex variables for new graduate students in mathematics.Includes complete proofs of Oka‘s Three Coheren
圖書(shū)封面Titlebook: Analytic Function Theory of Several Variables; Elements of Oka’s Co Junjiro Noguchi Textbook 2016 Springer Science+Business Media Singapore
影響因子The purpose of this book is to present the classical analytic function theory of several variables as a standard subject in a course of mathematics after learning the elementary materials (sets, general topology, algebra, one complex variable). This includes the essential parts of Grauert–Remmert‘s two volumes, GL227(236) (.Theory of Stein spaces.) and GL265 (.Coherent analytic sheaves.) with a lowering of the level for novice graduate students (here, Grauert‘s direct image theorem is limited to the case of finite maps)..The core of the theory is "Oka‘s Coherence", found and proved by Kiyoshi Oka. It is indispensable, not only in the study of complex analysis and complex geometry, but also in a large area of modern mathematics. In this book, just after an introductory chapter on holomorphic functions (Chap. 1), we prove Oka‘s First Coherence Theorem for holomorphic functions in Chap. 2. This defines a unique character of the book compared with other books on this subject, in which the notion of coherence appears much later..The present book, consisting of nine chapters, gives complete treatments of the following items: Coherence of sheaves of holomorphic functions (Chap. 2); Oka–Ca
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發(fā)表于 2025-3-21 23:05:19 | 只看該作者
Domains of Holomorphy,omain analytically extend over . (no Hartogs’ phenomenon happens at any boundary point). We first discuss the logarithmic convexity of Reinhardt domains, where every holomorphic function is expanded to a convergent power series. We prove that a domain is holomorphically convex if and only if it is a
板凳
發(fā)表于 2025-3-22 01:13:21 | 只看該作者
Analytic Sets and Complex Spaces,nce Theorem”, claiming the coherence of a geometric ideal sheaf (the ideal sheaf of an analytic set). By making use of it, the subset of singular points of an analytic set is proved to be an analytic subset of lower dimension. In the latter half, the notion of a complex space is introduced. Oka’s no
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,Cohomology of Coherent Sheaves and Kodaira’s Embedding Theorem, topology in the space of sections of a coherent sheaf. As a consequence we will see that all cohomologies of a coherent sheaf over a compact complex space are finite dimensional (Cartan–Serre Theorem). Furthermore, we will extend Grauert’s Theorem?. for a general coherent sheaf. Then, as an applica
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Correction to: Analytic Function Theory of Several Variables,
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Erratum to: Analytic Function Theory of Several Variables,
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Textbook 2016ter learning the elementary materials (sets, general topology, algebra, one complex variable). This includes the essential parts of Grauert–Remmert‘s two volumes, GL227(236) (.Theory of Stein spaces.) and GL265 (.Coherent analytic sheaves.) with a lowering of the level for novice graduate students (
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