Introduction to Complex Analysis in Several Variables / by Volker Scheidemann.

Springer eBooks

Elementary theory of several complex variables -- Continuation on circular and polycircular domains -- Biholomorphic maps -- Analytic Sets -- Hartogs’ Kugelsatz -- Continuation on Tubular Domains -- Cartan-Thullen Theory -- Local Properties of holomorphic functions.

This book gives a comprehensive introduction to complex analysis in several variables. It clearly focusses on special topics in complex analysis rather than trying to encompass as much material as possible. Many cross-references to other parts of mathematics, such as functional analysis or algebras, are pointed out in order to broaden the view and the understanding of the chosen topics. A major focus is extension phenomena alien to the one-dimensional theory, which are expressed in the famous Hartog's Kugelsatz, the theorem of Cartan-Thullen, and Bochner's theorem. The book primarily aims at students starting to work in the field of complex analysis in several variables and teachers who want to prepare a course. To that end, a lot of examples and supporting exercises are inserted throughout the text, which will help students to become acquainted with the subject.

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