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A theoretical framework for wavelet analysis in a Hermitean Clifford setting. (English) Zbl 1149.30036
The authors have developed an interesting Hermite-Clifford setting for Clifford analysis [e.g. F. Brackx, N. De Schepper and F. Sommen, J. Nat. Geom. 24, No. 1–2, 81–100 (2003; Zbl 1044.65096)]. This theory focusses on monogenic functions taking values in a complex Clifford algebra or in a complex spinor space. The monogenicity is given by the kernel of two complex mutually adjoint Dirac operators. In this paper the so-called zonal functions and plane waves are studied within the Hermite-Clifford setting. Of special interest are new Hermite polynomials which may serve as mother wavelets in a Hermitean theory, what has to be developed.

30G35 Functions of hypercomplex variables and generalized variables
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
44A15 Special integral transforms (Legendre, Hilbert, etc.)
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