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

By Junjiro Noguchi

ISBN-10: 9811002894

ISBN-13: 9789811002892

The goal of this publication is to give the classical analytic functionality conception of numerous variables as a regular topic in a process arithmetic after studying the user-friendly fabrics (sets, common topology, algebra, one advanced variable). This comprises the basic elements 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 snapshot theorem is restricted to the case of finite maps).
The middle of the speculation is "Oka's Coherence", came upon and proved by way of Kiyoshi Oka. it's imperative, not just within the learn of advanced research and intricate geometry, but additionally in a wide quarter of recent arithmetic. during this publication, simply after an introductory bankruptcy on holomorphic capabilities (Chap. 1), we turn out Oka's First Coherence Theorem for holomorphic features in Chap. 2. This defines a distinct personality of the booklet in comparison with different books in this topic, during which the idea of coherence appears to be like a lot later.
The current booklet, inclusive of 9 chapters, supplies 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 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 idea of complicated analytic subsets. bankruptcy eight is dedicated to the purposes of previously bought 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 all the above matters in a very self-contained demeanour. within the current quantity, a few classical proofs are more desirable and simplified, in order that the contents are simply obtainable 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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