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Spherical Means and Distributions in Clifford Analysis

  • Fred Brackx
  • Richard Delanghe
  • Frank Sommen
Chapter
Part of the Trends in Mathematics book series (TM)

Abstract

This paper consists of two parts. In the first part we deal with specific higher dimensional distributions within the framework of Clifford analysis. These distributions are “classical” in the sense that they were already introduced, albeit dispersed, in the literature on harmonic analysis and on Clifford analysis. Amongst these classical distributions are the fundamental solutions of the natural powers of the Laplace and the Dirac operators, and the integral kernel of the Hilbert transform. The strength of our approach is its unifying character.

In the second part new higher dimensional distributions are introduced, generalizing the distributions of part I. Crucial to this generalization is the use of so-called surface spherical monogenics. The whole picture thus obtained offers structural clarity and unity.

Keywords

Distributions spherical means Clifford analysis 

Mathematics Subject Classification (2000)

Primary 30G35 Secondary 46F10 

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References

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Copyright information

© Springer Basel AG 2004

Authors and Affiliations

  • Fred Brackx
    • 1
  • Richard Delanghe
    • 1
  • Frank Sommen
    • 1
  1. 1.Department of Mathematical AnalysisGhent UniversityGentBelgium

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