Download e-book for kindle: Analytic Function Theory of Several Variables: Elements of by Junjiro Noguchi

By Junjiro Noguchi

ISBN-10: 9811002894

ISBN-13: 9789811002892

The objective of this e-book is to offer the classical analytic functionality idea of a number of variables as a regular topic in a process arithmetic after studying the user-friendly fabrics (sets, normal topology, algebra, one complicated variable). This contains the basic components 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 speculation is "Oka's Coherence", stumbled on and proved through Kiyoshi Oka. it really is essential, not just within the learn of advanced research and complicated geometry, but in addition in a wide sector of recent arithmetic. during this publication, simply after an introductory bankruptcy on holomorphic features (Chap. 1), we turn out Oka's First Coherence Theorem for holomorphic services in Chap. 2. This defines a special personality of the publication in comparison with different books in this topic, during which the idea of coherence looks a lot later.
The current booklet, which includes 9 chapters, offers entire remedies of the next goods: Coherence of sheaves of holomorphic features (Chap. 2); Oka–Cartan's primary 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 offered (Chaps. three, 5). bankruptcy 6 offers with the speculation of advanced analytic subsets. bankruptcy eight is dedicated to the functions of previously acquired effects, proving Cartan–Serre's Theorem and Kodaira's Embedding Theorem. In Chap. nine, we talk about the ancient 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 stronger 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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