基于Clifford-Fourier变换的不确定原理  

Uncertainty principle for the Clifford-Fourier transform

作　　者：李珊珊 费铭岗[2] LI Shanshan;FEI Minggang(School of Computer Science and Technology, Southwest Minzu University, Chengdu 610041, China;School of Mathematical Science, University of Electronic Science and Technology of China, Chengdu 611731, China)

机构地区：[1]西南民族大学计算机科学与技术学院,成都610041 [2]电子科技大学数学科学学院,成都611731

出　　处：《黑龙江大学自然科学学报》2019年第3期297-303,共7页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the National Natural Science Foundation of China(11571083);the Fundamental Research Funds for the Central Universities,Southwest Minzu University(2015NZYQN27)

摘　　要：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.

关 键 词：不确定原理 Clifford-Fourier变换 CLIFFORD分析 向量值函数 

分 类 号：O174.22[理学—数学]