Clifford Algebra-Valued Wavelet Transform on Multivector Fields |
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Authors: | Mawardi Bahri Sriwulan Adji Jiman Zhao |
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Institution: | 1. School of Mathematical Sciences, Universiti Sains Malaysia, 11800, Penang, Malaysia 2. Department of Mathematics, Hasanuddin University, Tamalanrea, Makassar, Indonesia 3. School of Mathematical Sciences, Key Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing, 100875, China
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Abstract: | This paper presents a construction of the n = 2 (mod 4) Clifford algebra Cl
n,0-valued admissible wavelet transform using the admissible similitude group SIM(n), a subgroup of the affine group of
\mathbbRn{\mathbb{R}^{n}} . We express the admissibility condition in terms of the Cl
n,0 Clifford Fourier transform (CFT). We show that its fundamental properties such as inner product, norm relation, and inversion
formula can be established whenever the Clifford admissible wavelet satisfies a particular admissibility condition. As an
application we derive a Heisenberg type uncertainty principle for the Clifford algebra Cl
n,0-valued admissible wavelet transform. Finally, we provide some basic examples of these extended wavelets such as Clifford
Morlet wavelets and Clifford Hermite wavelets. |
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Keywords: | |
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