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.

中文翻译：

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Clifford分析中的两面傅里叶变换及其应用

在本文中，我们首先定义了双面Clifford Fourier变换（CFT）及其在\（L ^ {1} \）空间上的逆变换。然后研究了双面CFT的微分，\（F \ {h \} \）的k次方，Plancherel身份和双面CFT的时频偏移。最后，我们讨论了双面CFT的不确定性原理，并将其应用于偏微分方程。