Authors: Bahri Mawardi, Eckhard Hitzer
First, the basic concept of the vector derivative in geometric algebra is introduced. Second, beginning with the Fourier transform on a scalar function we generalize to a real Fourier transform on Clifford multivector-valued functions (f: R^3 -> Cl(3,0)). Third, we show a set of important properties of the Clifford Fourier transform on Cl(3,0) such as differentiation properties, and the Plancherel theorem. Finally, we apply the Clifford Fourier transform properties for proving an uncertainty principle for Cl(3,0) multivector functions. Keywords: vector derivative, multivector-valued function, Clifford (geometric) algebra, Clifford Fourier transform, uncertainty principle.
Comments: 23 Pages. Advances in Applied Clifford Algebras, 16(1), pp. 41-61 (2006). DOI 10.1007/s00006-006-0003-x , 3 tables.
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