Holomorphic Functions in the Plane and n-dimensional Space

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

The present book is very well and enthusiastically written and in many details marvellously elaborated. This is in particular the case for the typographically exposed historical remarks including photos of some of the main initiators of the number systems etc. involved. [...]

This book is recommended as a text book for basic courses in complex analysis and also for self studies.

Review of the German edition

Heinrich Begehr (Berlin), Zentralblatt MATH

• Institut für Angewandte Mathematik Bauhaus-Universität Weimar, Weimar, Germany

  Klaus Gürlebeck

• Lehrstuhl II für Mathematik, RWTH Aachen, Aachen, Germany

  Klaus Habetha

• Institut für Angewandte Analysis Fakultät für Mathematik, TU Bergakademie Freiberg, Freiberg, Germany

  Wolfgang Sprößig