Junjiro Noguchi's Analytic Function Theory of Several Variables: Elements of PDF

By Junjiro Noguchi

ISBN-10: 9811002894

ISBN-13: 9789811002892

The objective of this publication is to provide the classical analytic functionality concept of numerous variables as a typical topic in a process arithmetic after studying the common fabrics (sets, basic topology, algebra, one advanced variable). This contains the fundamental elements of Grauert–Remmert's volumes, GL227(236) (Theory of Stein spaces) and GL265 (Coherent analytic sheaves) with a decreasing of the extent for beginner graduate scholars (here, Grauert's direct photograph theorem is restricted to the case of finite maps).
The center of the idea is "Oka's Coherence", stumbled on and proved through Kiyoshi Oka. it's necessary, not just within the learn of complicated research and intricate geometry, but additionally in a wide sector 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 capabilities in Chap. 2. This defines a different personality of the e-book in comparison with different books in this topic, during which the idea of coherence seems to be a lot later.
The current e-book, inclusive of 9 chapters, supplies entire remedies of the next goods: Coherence of sheaves of holomorphic features (Chap. 2); Oka–Cartan's basic Theorem (Chap. 4); Coherence of excellent 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 awarded (Chaps. three, 5). bankruptcy 6 offers with the idea of advanced 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 talk about the historic improvement of "Coherence".
It is hard to discover a e-book at this point that treats all the above matters in a totally self-contained demeanour. within the current quantity, a couple of classical proofs are more advantageous 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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