Download Analytic Function Theory of Several Variables: Elements of by Junjiro Noguchi PDF

By Junjiro Noguchi

The objective of this ebook is to give the classical analytic functionality idea of a number of variables as a typical topic in a process arithmetic after studying the effortless fabrics (sets, basic topology, algebra, one complicated variable). This comprises the fundamental 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 snapshot theorem is proscribed to the case of finite maps).
The middle of the idea is "Oka's Coherence", came upon and proved by way of Kiyoshi Oka. it's fundamental, not just within the examine of advanced research and complicated geometry, but additionally in a wide quarter of recent arithmetic. during this ebook, simply after an introductory bankruptcy on holomorphic capabilities (Chap. 1), we end up Oka's First Coherence Theorem for holomorphic features in Chap. 2. This defines a distinct personality of the e-book in comparison with different books in this topic, during which the proposal of coherence seems a lot later.
The current ebook, which includes 9 chapters, offers whole remedies of the next goods: Coherence of sheaves of holomorphic capabilities (Chap. 2); Oka–Cartan's primary Theorem (Chap. 4); Coherence of perfect 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 offered (Chaps. three, 5). bankruptcy 6 bargains with the idea of advanced analytic subsets. bankruptcy eight is dedicated to the purposes of previously received 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 few classical proofs are greater and simplified, in order that the contents are simply obtainable for starting graduate students.

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