© 2011

Holomorphic Function Theory in Several Variables

An Introduction


Table of contents

  1. Front Matter
    Pages i-xiii
  2. Christine Laurent-Thiébaut
    Pages 21-55
  3. Christine Laurent-Thiébaut
    Pages 75-93
  4. Christine Laurent-Thiébaut
    Pages 95-112
  5. Christine Laurent-Thiébaut
    Pages 113-145
  6. Back Matter
    Pages 211-252

About this book


This book provides an introduction to complex analysis in several variables. The viewpoint of integral representation theory together with Grauert's bumping method offers a natural extension of single variable techniques to several variables analysis and leads rapidly to important global results. Applications focus on global extension problems for CR functions, such as the Hartogs-Bochner phenomenon and removable singularities for CR functions. Three appendices on differential manifolds, sheaf theory and functional analysis make the book self-contained.

Each chapter begins with a detailed abstract, clearly demonstrating the structure and relations of following chapters. New concepts are clearly defined and theorems and propositions are proved in detail. Historical notes are also provided at the end of each chapter.

Clear and succinct, this book will appeal to post-graduate students, young researchers seeking an introduction to holomorphic function theory in several variables and lecturers seeking a concise book on the subject.


Extension of CR functions Integral formulas Levi problem Several complex variables

Authors and affiliations

  1. 1.Université Joseph FourierSaint Martin d'Héres CedexFrance

Bibliographic information

  • Book Title Holomorphic Function Theory in Several Variables
  • Book Subtitle An Introduction
  • Authors Christine Laurent-Thiébaut
  • DOI
  • Copyright Information Springer-Verlag London Limited 2011
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Softcover ISBN 978-0-85729-029-8
  • eBook ISBN 978-0-85729-030-4
  • Edition Number 1
  • Number of Pages XIII, 252
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information Original French edition published by EDP Sciences, CNRS Editions, France, 1997
  • Topics Several Complex Variables and Analytic Spaces
  • Buy this book on publisher's site


From the reviews:

“This introduction to complex analysis in several variables uses integral representation theory together with Grauert’s bumping method to characterize domains of holomorphy, in other words to solve the Levi problem. … Each part is provided with a detailed abstract and interesting historical notes. This concise and self-contained book is a welcome enrichment to the existing literature for both graduate students as well as researchers.” (F. Haslinger, Monatshefte für Mathematik, Vol. 165 (1), January, 2012)