Introduction to Complex Analysis in Several Variables

Beschreibung

This book gives a comprehensive introduction to complex analysis in several variables. While it focusses on a number of topics in complex analysis rather than trying to cover as much material as possible, references to other parts of mathematics such as functional analysis or algebras are made to help broaden the view and the understanding of the chosen topics. A major focus are 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 aims primarily at students starting to work in the field of complex analysis in several variables and instructors preparing a course. To that end, a lot of examples and supporting exercises are provided throughout the text.

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.

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«

“The book under review is intended to be a first course in several complex variables for a reader to get an overview of (a selection of topics) in several complex variables. ...  I very much recommend the book as a first several complex variables course.” (Jasna Prezelj, zbMATH 1530.32001, 2024)

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