Download e-book for kindle: Analytic Function Theory of Several Variables: Elements of by Junjiro Noguchi

By Junjiro Noguchi

The objective of this publication is to offer the classical analytic functionality concept of numerous variables as a regular topic in a process arithmetic after studying the simple fabrics (sets, normal topology, algebra, one complicated variable). This comprises the basic elements of Grauert–Remmert's volumes, GL227(236) (Theory of Stein spaces) and GL265 (Coherent analytic sheaves) with a decreasing of the extent for beginner graduate scholars (here, Grauert's direct photo theorem is proscribed to the case of finite maps).
The middle of the idea is "Oka's Coherence", chanced on and proved by means of Kiyoshi Oka. it's necessary, not just within the research of advanced research and intricate geometry, but additionally in a wide zone of contemporary arithmetic. during this publication, simply after an introductory bankruptcy on holomorphic features (Chap. 1), we turn out Oka's First Coherence Theorem for holomorphic features in Chap. 2. This defines a special personality of the publication in comparison with different books in this topic, during which the thought of coherence appears to be like a lot later.
The current booklet, which includes 9 chapters, offers entire remedies of the subsequent goods: Coherence of sheaves of holomorphic capabilities (Chap. 2); Oka–Cartan's basic Theorem (Chap. 4); Coherence of excellent sheaves of advanced analytic subsets (Chap. 6); Coherence of the normalization sheaves of advanced areas (Chap. 6); Grauert's Finiteness Theorem (Chaps. 7, 8); Oka's Theorem for Riemann domain names (Chap. 8). The theories of sheaf cohomology and domain names of holomorphy also are provided (Chaps. three, 5). bankruptcy 6 bargains with the speculation of advanced analytic subsets. bankruptcy eight is dedicated to the purposes of previously bought effects, proving Cartan–Serre's Theorem and Kodaira's Embedding Theorem. In Chap. nine, we speak about the ancient improvement of "Coherence".
It is tough to discover a publication at this point that treats the entire above topics in a totally self-contained demeanour. within the current quantity, a couple of classical proofs are greater and simplified, in order that the contents are simply obtainable for starting graduate students.

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Analytic Function Theory of Several Variables: Elements of - download pdf or read online

The aim of this booklet is to offer the classical analytic functionality idea of a number of variables as a typical topic in a process arithmetic after studying the trouble-free fabrics (sets, basic topology, algebra, one advanced variable). This contains the basic components of Grauert–Remmert's volumes, GL227(236) (Theory of Stein areas) and GL265 (Coherent analytic sheaves) with a decreasing of the extent for beginner graduate scholars (here, Grauert's direct photo theorem is restricted to the case of finite maps).

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Analytic Function Theory of Several Variables: Elements of Oka’s Coherence by Junjiro Noguchi


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