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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.

MSC:
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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