Holomorphic Functions in the Plane and n-dimensional Space

  • Klaus Gürlebeck
  • Klaus Habetha
  • Wolfgang Sprößig

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Pages 1-72
  3. Pages 73-124
  4. Back Matter
    Pages 323-394

About this book


Complex analysis nowadays has higher-dimensional analoga: the algebra of complex numbers is replaced then by the non-commutative algebra of real quaternions or by Clifford algebras. During the last 30 years the so-called quaternionic and Clifford or hypercomplex analysis successfully developed to a powerful theory with many applications in analysis, engineering and mathematical physics. This textbook introduces both to classical and higher-dimensional results based on a uniform notion of holomorphy. Historical remarks, lots of examples, figures and exercises accompany each chapter.


Clifford algebra Clifford analysis Complex analysis holomorphic function orthogonal decomposition

Authors and affiliations

  • Klaus Gürlebeck
    • 1
  • Klaus Habetha
    • 2
  • Wolfgang Sprößig
    • 3
  1. 1.Institut für Angewandte Mathematik Bauhaus-Universität WeimarWeimarGermany
  2. 2.Lehrstuhl II für MathematikRWTH AachenAachenGermany
  3. 3.Institut für Angewandte Analysis Fakultät für MathematikTU Bergakademie FreibergFreibergGermany

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