Abstract
In this paper, we first define a two-sided Clifford Fourier transform(CFT) and its inverse transformation on $$L^{1}$$ space. Then we study the differential of the two-sided CFT, the k-th power of $$F \{h\}$$ , Plancherel identity and time-frequency shift of the two-sided CFT. Finally we discuss the uncertainty principle of the two-sided CFT and give an application of the two-sided CFT to a partial differential equation.
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