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

By Junjiro Noguchi

The function of this ebook is to give the classical analytic functionality conception of a number of variables as a regular topic in a process arithmetic after studying the simple fabrics (sets, normal topology, algebra, one advanced variable). This comprises the basic components of Grauert–Remmert's volumes, GL227(236) (Theory of Stein spaces) and GL265 (Coherent analytic sheaves) with a reducing of the extent for beginner graduate scholars (here, Grauert's direct photograph theorem is restricted to the case of finite maps).
The middle of the idea is "Oka's Coherence", discovered and proved via Kiyoshi Oka. it really is integral, not just within the examine of complicated research and complicated geometry, but in addition in a wide zone of contemporary arithmetic. during this e-book, simply after an introductory bankruptcy on holomorphic services (Chap. 1), we end up Oka's First Coherence Theorem for holomorphic capabilities in Chap. 2. This defines a special personality of the ebook in comparison with different books in this topic, during which the suggestion of coherence seems to be a lot later.
The current booklet, such as 9 chapters, provides entire remedies of the subsequent 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 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 old improvement of "Coherence".
It is tough to discover a booklet 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 stronger and simplified, in order that the contents are simply obtainable for starting graduate students.

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