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

By Junjiro Noguchi

The objective of this ebook is to offer the classical analytic functionality idea of a number of variables as a customary topic in a process arithmetic after studying the basic fabrics (sets, common 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 photograph theorem is proscribed to the case of finite maps).
The center of the idea is "Oka's Coherence", stumbled on and proved by way of Kiyoshi Oka. it really is vital, not just within the examine of complicated research and intricate geometry, but in addition in a wide region of recent arithmetic. during this booklet, simply after an introductory bankruptcy on holomorphic features (Chap. 1), we end up Oka's First Coherence Theorem for holomorphic capabilities in Chap. 2. This defines a distinct personality of the publication in comparison with different books in this topic, during which the suggestion of coherence seems to be a lot later.
The current publication, which includes 9 chapters, offers entire remedies of the next goods: Coherence of sheaves of holomorphic services (Chap. 2); Oka–Cartan's basic Theorem (Chap. 4); Coherence of excellent sheaves of complicated analytic subsets (Chap. 6); Coherence of the normalization sheaves of complicated 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 complicated analytic subsets. bankruptcy eight is dedicated to the functions of previously received effects, proving Cartan–Serre's Theorem and Kodaira's Embedding Theorem. In Chap. nine, we talk about the ancient improvement of "Coherence".
It is tough to discover a ebook at this point that treats all the above matters in a very self-contained demeanour. within the current quantity, a couple of classical proofs are greater and simplified, in order that the contents are simply available for starting graduate students.

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