02706nam 22004935a 450 991015193530332120260720163903.03-03719-549-510.4171/049(CKB)3710000000953822(CH-001817-3)75-091109(PPN)178155373(DE-4084)10.4171/049(EXLCZ)99371000000095382220080303j20080303 fy 0engurnn|mmmmamaatxtrdacontentcrdamediacrrdacarrierFirst Steps in Several Complex Variables: Reinhardt DomainsEMS Press20081 online resource (367 pages)EMS Textbooks in Mathematics (etb)62943-49559783037190494 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.First Steps in Several Complex VariablesCalculus & mathematical analysisbicsscSeveral complex variables and analytic spacesmscCalculus & mathematical analysisSeveral complex variables and analytic spaces32-01msc32A05msc32A10msc32D05msc32E05msc32F45mscJarnickiaut2014682Pflug PeterDE-4084BOOK9910151935303321First Steps in Several Complex Variables: Reinhardt Domains4805317UNINA