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 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.
Mathematics Subject Classification (2010). Primary 30G35, 43A32; Secondary 33C80, 31A05.
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© 2011 Springer Basel AG
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Li, S., Fei, M. (2011). Bochner’s Formulae for Dunkl-Harmonics and Dunkl-Monogenics. In: Sabadini, I., Sommen, F. (eds) Hypercomplex Analysis and Applications. Trends in Mathematics. Springer, Basel. https://doi.org/10.1007/978-3-0346-0246-4_11
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DOI: https://doi.org/10.1007/978-3-0346-0246-4_11
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Publisher Name: Springer, Basel
Print ISBN: 978-3-0346-0245-7
Online ISBN: 978-3-0346-0246-4
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