Complex Analysis and Operator Theory

, Volume 6, Issue 5, pp 1047–1067 | Cite as

The Fractional Clifford-Fourier Transform

  • Hendrik De BieEmail author
  • Nele De Schepper


In this paper, a fractional version of the Clifford-Fourier transform is introduced, depending on two numerical parameters. A series expansion for the kernel of the resulting integral transform is derived. In the case of even dimension, also an explicit expression for the kernel in terms of Bessel functions is obtained. Finally, the analytic properties of this new integral transform are studied in detail.


Clifford-Fourier transform Fractional transform Integral kernel Clifford analysis 

Mathematics Subject Classification

30G35 42B10 


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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Department of Mathematical Analysis, Faculty of Engineering and ArchitectureGhent UniversityGentBelgium

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