Introduction to Complex Analysis in Several Variables

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 second edition includes hints and suggestions for the solution of the provided exercises, with various degrees of support.

Focused on students Requires minimum of prerequisites More than 50 examples, over 100 exercises

Autorentext

Volker Scheidemann ist Professor am Lehrstuhl für Informatik und Wirtschaftsinformatik an der Provadis School of International Management and Technology. Bevor er Professor wurde, war er rund 20 Jahre in der Informationssicherheit tätig und spezialisierte sich auf angewandte Kryptographie und Security Awareness. Er ist ein renommierter Referent auf Konferenzen und führt zusammen mit seiner Frau in ihrer Agentur Scheidemann Training Workshops und Trainings durch. Für sein Lehrformat "Escape Room" wurde er mit dem Preis für kompetenzorientiertes Unterrichten ausgezeichnet. Als begeisterter Lindy Hop Tänzer lehnt er sein Lehrmotto an einen alten Swing-Klassiker an: "T'ain't what you do, it's the way that you do it - that's what gets results!"

Inhalt

• 1. Elementary Theory of Several Complex Variables. - 2. Continuation on Circular and Polycircular Domains. - 3. Biholomorphic Maps. - 4. Analytic Sets. - 5. Hartogs' Kugelsatz. - 6. Continuation on Tubular Domains. - 7. CartanThullen Theory. - 8. Local Properties of Holomorphic Functions. - 9. Hints to the Exercises.