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Birkhäuser

Introduction to Complex Analysis in Several Variables

  • Book
  • © 2005

Overview

Authors:
  1. Volker Scheidemann

    1. Marburg, Germany

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  • Focused on students
  • Requires minimum of prerequisites
  • More than 50 examples, over 100 exercises
  • Includes supplementary material: sn.pub/extras

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-viii
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  2. Elementary theory of several complex variables

    Pages 1-46

  3. Continuation on circular and polycircular domains

    Pages 47-57

  4. Biholomorphic maps

    Pages 59-69

  5. Analytic Sets

    Pages 71-77

  6. Hartogs’ Kugelsatz

    Pages 79-96

  7. Continuation on Tubular Domains

    Pages 97-109

  8. Cartan-Thullen Theory

    Pages 111-124

  9. Local Properties of holomorphic functions

    Pages 125-163

  10. Back Matter

    Pages 165-171
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Keywords

About this book

The idea for this book came when I was an assistant at the Department of Mat- matics and Computer Science at the Philipps-University Marburg, Germany. S- eraltimesIfacedthetaskofsupportinglecturesandseminarsoncomplexanalysis of several variables and found out that there are very few books on the subject, compared to the vast amount of literature on function theory of one variable, let alone on real variables or basic algebra. Even fewer books, to my understanding, were written primarily with the student in mind. So it was quite hard to ?nd s- porting examples and exercises that helped the student to become familiar with the fascinating theory of several complex variables. Of course, there are notable exceptions, like the books of R.M. Range [9] or B. and L. Kaup [6], however, even those excellent books have a drawback: they are quite thick and thus quite expensive for a student’s budget. So an additional motivation to write this book was to give a comprehensive introduction to the theory of several complex variables, illustrate it with as many examples as I could ?nd and help the student to get deeper insight by giving lots of exercises, reaching from almost trivial to rather challenging. There are not many illustrations in this book, in fact, there is exactly one, becauseinthetheoryofseveralcomplexvariablesI?ndmostofthemeithertrivial or misleading. The readers are of course free to have a di?erent opinion on these matters.

Reviews

This is a book written with the student in mind: it offers a concise treatment of complex analysis in several variables, by focusing on special topics rather than trying to be a comprehensive treatment of the subject. (...) The main importance of this book is the fact that it fills a void: there are relatively few books on several complex variables. Any (graduate) student beginning work in this area and any instructor considering teaching a course in several complex variables should definitely take a look at Professor Scheidemann's work.

MAA-Reviews

Authors and Affiliations

  • Marburg, Germany

    Volker Scheidemann

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