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Birkhäuser

Holomorphic Functions in the Plane and n-dimensional Space

  • Textbook
  • © 2008

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Overview

  • First textbook on elementary level introducing to classical complex analysis and its generalizations at the same time
  • Includes supplementary material: sn.pub/extras

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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.

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Table of contents (4 chapters)

Reviews

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

Authors and Affiliations

  • 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

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