Introduction to Complex Analysis in Several Variables

Beschreibung

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.

This book gives a comprehensive introduction to complex analysis in several variables. One major focus of the book is extension phenomena alien to the one-dimensional theory (Hartog's Kugelsatz, theorem of Cartan-Thullen, 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 university lecture. Therefore, the book contains more than 50 examples and more than supporting exercises.

Focused on students

Requires minimum of prerequisites

More than 50 examples, over 100 exercises

Includes supplementary material: sn.pub/extras

Autor*in

Volker Scheidemann

Themen in »Introduction to Complex Analysis in Several Variables«

Biholomorphic maps Cartan-Thullen theory Complex analysis Complex variables Holomorphic functions Kugelsatz

Stimmen zu »Introduction to Complex Analysis in Several Variables«

This is a book written with the student in mind: it offers a concise treatment of complex analysis in several variables, by focusing on special topics rather than trying to be a comprehensive treatment of the subject. (...) The main importance of this book is the fact that it fills a void: there are relatively few books on several complex variables. Any (graduate) student beginning work in this area and any instructor considering teaching a course in several complex variables should definitely take a look at Professor Scheidemann's work.

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