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

By Junjiro Noguchi

The goal of this e-book is to offer the classical analytic functionality concept of numerous variables as a typical topic in a process arithmetic after studying the straightforward fabrics (sets, basic topology, algebra, one complicated variable). This comprises 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 amateur graduate scholars (here, Grauert's direct picture theorem is restricted to the case of finite maps).
The center of the speculation is "Oka's Coherence", came upon and proved via Kiyoshi Oka. it really is crucial, not just within the examine of advanced research and complicated geometry, but additionally in a wide sector of contemporary arithmetic. during this e-book, simply after an introductory bankruptcy on holomorphic capabilities (Chap. 1), we end up Oka's First Coherence Theorem for holomorphic services in Chap. 2. This defines a distinct personality of the e-book in comparison with different books in this topic, during which the inspiration of coherence seems to be a lot later.
The current ebook, along with 9 chapters, supplies 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 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 speculation of advanced analytic subsets. bankruptcy eight is dedicated to the functions of previously received effects, proving Cartan–Serre's Theorem and Kodaira's Embedding Theorem. In Chap. nine, we talk about the ancient improvement of "Coherence".
It is tough to discover a booklet at this point that treats all the above topics 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 available for starting graduate students.

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