Introduction to Complex Analysis in Several Variables

ISBN-13: 9783031264276 / Angielski

Volker Scheidemann

Opis

This book provides 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 100 supporting exercises.

Spis treści

- 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. 

- Hints to the exercises.

O autorze

​Volker Scheidemann is a professor at the department for informatics and business informatics at Provadis School of International Management and Technology. Before becoming professor, he has been working in information security for about 20 years specializing in applied cryptography and security awareness. He is a renowned speaker at conferences and conducts workshops and trainings together with his wife in their agency Scheidemann Training. He holds an award for competence-oriented teaching for his teaching format ‘Escape Room’. Being an enthusiastic Lindy Hop dancer he borrows his teaching motto from an old Swing classic: “T’ain’t what you do, it’s the way that you do it – that’s what gets results!”

Blurb

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.