Clifford Fourier Transformation and Uncertainty Principle for the Clifford Geometric Algebra Cl 3,0 |
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Authors: | Bahri Mawardi Eckhard MS Hitzer |
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Affiliation: | (1) Department of Applied Physics, University of Fukui, Bunkyo 3-9-1, Fukui City 910-8507, Japan |
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Abstract: | 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 Third, we show a set of important properties of the Clifford Fourier transform on Cl3,0 such as differentiation properties, and the Plancherel theorem. Finally, we apply the Clifford Fourier transform properties for proving an uncertainty principle for Cl3,0 multivector functions. |
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Keywords: | vector derivative multivector-valued function Clifford (geometric) algebra Clifford Fourier transform uncertainty principle |
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