# First Steps in Several Complex Variables: Reinhardt Domains

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*Marek Jarnicki; Peter Pflug*

A publication of the European Mathematical Society

This book provides a comprehensive introduction to the field of several
complex variables in the setting of a very special but basic class of
domains, the so-called Reinhardt domains. In this way the reader may
learn much about this area without encountering too many technical
difficulties.

Chapter 1 describes the fundamental notions and the phenomenon of
simultaneous holomorphic extension. Chapter 2 presents a fairly complete
discussion of biholomorphisms of bounded (complete) Reinhardt domains in the
two dimensional case. The third chapter gives a classification of Reinhardt
domains of existence for the most important classes of holomorphic functions.
The last chapter deals with invariant functions and gives explicit calculations
of many of them on certain Reinhardt domains. Numerous exercises are included
to help the readers with their understanding of the material. Further results
and open problems are added which may be useful as seminar topics.

The primary aim of this book is to introduce students or non-experts to some
of the main research areas in several complex variables. The book provides a
friendly invitation to this field as the only prerequisite is a basic knowledge
of analysis.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

#### Readership

Undergraduates, graduate students, and research mathematicians interested in analysis.