Bochner’s Formulae for Dunkl-Harmonics and Dunkl-Monogenics
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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 hκ 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.
KeywordsReflection group Clifford algebra Dunkl transform Dunkl-harmonics Dunkl-monogenics
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