E.M.S. Hitzer, B. Mawardi

*Cl*_{n,0} , n = 3 (mod 4)

in T. Qian, M.I. Vai, X.Yusheng (eds.),
*Wavelet Analysis and Applications*,
Springer (SCI) Book Series *Applied and Numerical Harmonic Analysis*,
Springer (2006), pp. 45-54.

**Abstract:**
First, the basic concepts of the multivector functions, vector differential
and vector derivative in geometric algebra are introduced. Second,
we define a generalized real Fourier transform on Clifford multivector-valued
functions (f: R^n --> *Cl*_{n,0} , n = 3 (mod 4)). Third, we introduce a set of important
properties of the Clifford Fourier transform on *Cl*_{n,0} , n = 3 (mod 4)
such as differentiation properties, and the Plancherel theorem. Finally, we
apply the Clifford Fourier transform properties for proving a directional uncertainty
principle for *Cl*_{n,0} , n = 3 (mod 4) multivector functions.

**Mathematics Subject Classification (2000).** Primary 15A66; Secondary 43A32.

**Keywords.** Vector derivative, multivector-valued function, Clifford (geometric)
algebra, Clifford Fourier transform, uncertainty principle.

The original publication will be available at www.springerlink.com.

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