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Bochner’s Formulae for Dunkl-Harmonics and Dunkl-Monogenics

  • Shanshan LiEmail author
  • Minggang Fei
Conference paper
  • 688 Downloads
Part of the Trends in Mathematics book series (TM)

Abstract

We study the counterpart of a direct sum decomposition of L2(Rd) into subspaces which are invariant under the classical Fourier transform for the Dunkl transform associated with a family of weight functions which keep invariant under a given finite reflection group. The explicit Dunkl transform formula for each component of a function in L2(Rd; h2 κ) is established, which generalizes Bochner’s formulae for spherical harmonics and spherical monogenics in Dunkl case.

Keywords

Reflection group Clifford algebra Dunkl transform Dunkl-harmonics Dunkl-monogenics 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.School of Computer Science and TechnologySouthwest University for NationalitiesChengduP. R. China
  2. 2.School of Mathematical SciencesUniversity of Electronic Science and Technology of ChinaChengduP. R. China
  3. 3.Departamento de MatemáticaUniversidade de AveiroAveiroPortugal

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