B. Mawardi, E.M.S. Hitzer

*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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