Introduction to Complex Analysis in Several Variables

• Κύριος συγγραφέας: Scheidemann, Volker (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Basel : Birkhäuser Basel, 2005.
• Θέματα: Mathematics.; Functions of complex variables.; Functions of a Complex Variable.

 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. 

 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.