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

By Junjiro Noguchi

The goal of this publication is to offer the classical analytic functionality idea of numerous variables as a customary topic in a process arithmetic after studying the undemanding fabrics (sets, normal topology, algebra, one advanced variable). This contains 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 amateur 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", came across and proved by way of Kiyoshi Oka. it really is crucial, not just within the learn of advanced research and complicated geometry, but in addition in a wide sector of recent arithmetic. during this ebook, 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 different personality of the publication in comparison with different books in this topic, during which the thought of coherence seems a lot later.
The current booklet, including 9 chapters, supplies entire remedies of the subsequent goods: Coherence of sheaves of holomorphic features (Chap. 2); Oka–Cartan's primary Theorem (Chap. 4); Coherence of excellent sheaves of advanced 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 bargains with the idea of advanced analytic subsets. bankruptcy eight is dedicated to the purposes of previously got effects, proving Cartan–Serre's Theorem and Kodaira's Embedding Theorem. In Chap. nine, we speak about the old improvement of "Coherence".
It is hard to discover a publication at this point that treats all the above matters in a totally self-contained demeanour. within the current quantity, a few classical proofs are superior and simplified, in order that the contents are simply obtainable for starting graduate students.

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