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

By Junjiro Noguchi

The function of this booklet is to offer the classical analytic functionality idea of numerous variables as a regular topic in a process arithmetic after studying the straight forward fabrics (sets, basic topology, algebra, one complicated variable). This comprises the basic components of Grauert–Remmert's volumes, GL227(236) (Theory of Stein spaces) and GL265 (Coherent analytic sheaves) with a decreasing of the extent for amateur graduate scholars (here, Grauert's direct photo theorem is proscribed to the case of finite maps).
The middle of the speculation is "Oka's Coherence", stumbled on and proved by means of Kiyoshi Oka. it's vital, not just within the research of advanced research and complicated geometry, but additionally in a wide zone of recent arithmetic. during this ebook, simply after an introductory bankruptcy on holomorphic services (Chap. 1), we end up Oka's First Coherence Theorem for holomorphic services in Chap. 2. This defines a distinct personality of the booklet in comparison with different books in this topic, within which the concept of coherence seems a lot later.
The current booklet, along with 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 awarded (Chaps. three, 5). bankruptcy 6 offers with the speculation of advanced analytic subsets. bankruptcy eight is dedicated to the purposes of previously acquired effects, proving Cartan–Serre's Theorem and Kodaira's Embedding Theorem. In Chap. nine, we speak about the old improvement of "Coherence".
It is tough to discover a publication at this point that treats the entire above matters in a totally self-contained demeanour. within the current quantity, a couple of classical proofs are enhanced and simplified, in order that the contents are simply available for starting graduate students.

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

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