基于Clifford-Fourier变换的不确定原理

Uncertainty principle for the Clifford-Fourier transform

在Clifford分析框架下,考虑一种基于超李代数sop(1|2)的Clifford-Fourier变换,该超李代数包含经典李代数sl2为其偶子代数。介绍定义以及已有的相关性质,研究该变换与经典Fourier变换类似的性质,如微分公式、乘法公式、Plancherel定理以及Parsevel等式等。根据Holder不等式以及前面推导的结论,证明了Heisenberg-Pauli-Weyl型不确定原理。

In the framework of Clifford analysis, a generalized Clifford-Fourier transform is considered. This transform is given by a similar operator exponential as the classical Fourier transform but containing generators of Lie superalgebra sop(1|2)(containing Lie algebra sl 2 as its even subalgebra). Some further properties of the Clifford-Fourier transform, such as differential formula, multiplication formula, Plancherel Theorem and Parsevel’s Identity, are developed. As an application, a Heisenberg-Pauli-Weyl type uncertainty principle for the Clifford-Fourier transform is proven.