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Several versions of the Fourier transform have been formulated in theframework of Clifford algebra. We present a (Clifford-Fourier) transform,constructed using the geometric properties of Clifford algebra. We show thecorresponding results of operational calculus. We obtain a technique toconstruct monogenic extensions of a certain type of continuous functions, andversions of the Paley-Wiener theorems are formulated.

The Clifford-Fourier transform $\mathcal{F}_O$ and monogenic extensions