E.S.M. Hitzer

**Real Clifford Algebra Cl(n,0), n = 2,3(mod 4) Wavelet Transform**

edited by T.E. Simos et al.,
*AIP Proceedings of ICNAAM 2009*,
No. 1168, pp. 781-784 (2009).

**Abstract:**
We show how for n = 2,3(mod 4) continuous Clifford (geometric) algebra (GA)
Cl_n-valued admissible wavelets
can be constructed using the similitude group SIM(n).
We strictly aim for real geometric interpretation, and replace the
imaginary unit i element of C therefore with a GA blade squaring to
-1. Consequences due to non-commutativity arise. We express
the admissibility condition in terms of a Cl_n Clifford Fourier
Transform and then derive a set of important properties such as
dilation, translation and rotation covariance, a reproducing kernel,
and show how to invert the Clifford wavelet transform. As
an example, we introduce Clifford Gabor wavelets. We further invent a
generalized Clifford wavelet uncertainty principle.

**AMS Subj. Class.**
15A66, 42C40, 94A12

**Keywords.**
Clifford geometric algebra, Clifford wavelet transform,
multidimensional wavelets, continuous wavelets, similitude group.

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