Hypercomplex Analysis: New Perspectives and Applications

  • Swanhild Bernstein
  • Uwe Kähler
  • Irene Sabadini
  • Frank Sommen
Conference proceedings

Part of the Trends in Mathematics book series (TM)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Ricardo Abreu Blaya, Juan Bory Reyes, Alí Guzmán Adán, Uwe Kähler
    Pages 1-18
  3. Daniel Alpay, Fabrizio Colombo, Irene Sabadini, Guy Salomon
    Pages 43-59
  4. Eusebio Ariza, Antonio Di Teodoro
    Pages 61-73
  5. Swanhild Bernstein
    Pages 75-88
  6. Carmona L. Luís Javier, Lino Feliciano Reséndis Ocampo, Luis Manuel Tovar Sánchez
    Pages 89-110
  7. David Eelbode, Nikolaas Verhulst
    Pages 111-118
  8. Sirkka-Liisa Eriksson, Heikki Orelma, Nelson Vieira
    Pages 119-132
  9. Riccardo Ghiloni, Valter Moretti, Alessandro Perotti
    Pages 133-143
  10. Klaus Gürlebeck, Hung Manh Nguyen
    Pages 181-189
  11. Uwe Kähler, Nelson Vieira
    Pages 191-201
  12. Daniele C. Struppa, Adrian Vajiac, Mihaela B. Vajiac
    Pages 213-227

About these proceedings


Hypercomplex analysis is the extension of complex analysis to higher dimensions where the concept of a holomorphic function is substituted by the concept of a monogenic function. In recent decades this theory has come to the forefront of higher dimensional analysis. There are several approaches to this: quaternionic analysis which merely uses quaternions, Clifford analysis which relies on Clifford algebras, and generalizations of complex variables to higher dimensions such as split-complex variables. This book includes a selection of papers presented at the session on quaternionic and hypercomplex analysis at the ISAAC conference 2013 in Krakow, Poland. The topics covered represent new perspectives and current trends in hypercomplex analysis and applications to mathematical physics, image analysis and processing, and mechanics.


continuous and discrete Clifford analysis image processing quaternionic analysis representation theory

Editors and affiliations

  • Swanhild Bernstein
    • 1
  • Uwe Kähler
    • 2
  • Irene Sabadini
    • 3
  • Frank Sommen
    • 4
  1. 1.Institute of Applied AnalysisTU Bergakademie FreibergFreibergGermany
  2. 2.Departamento de MatemáticaUniversidade de AveiroAveiroPortugal
  3. 3.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly
  4. 4.Dept. Mathematical AnalysisUniversity of GentGentBelgium

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-08770-2
  • Online ISBN 978-3-319-08771-9
  • Series Print ISSN 2297-0215
  • Series Online ISSN 2297-024X
  • Buy this book on publisher's site