B. Mawardi, E.M.S. Hitzer
Clifford Fourier Transformation and Uncertainty Principle for the Clifford Geometric Algebra Cl_{3,0}
Advances in Applied Clifford Algebras, 16(1), pp. 41-61 (2006).

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 (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.

The original publication is available at www.springerlink.com. doi:10.1007/s00006-006-0003-x


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