Clifford Fourier transformation and uncertainty principle for the Clifford geometric algebra Cl3,0

被引：60

作者：

Mawardi, Bahri ^{[1
]}

Hitzer, Eckhard M. S. ^{[1
]}

机构：

[1] Univ Fukui, Dept Appl Phys, Fukui 9108507, Japan

来源：

ADVANCES IN APPLIED CLIFFORD ALGEBRAS | 2006年 / 16卷 / 01期

关键词：

vector derivative; multivector-valued function; Clifford (geometric) algebra; Clifford Fourier transform; uncertainty principle;

D O I：

10.1007/s00006-006-0003-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

First, the basic concept of the vector derivative in geometric algebra is introduced. Second, beginning with the Fourier transform on a scalar function we generalize to a real Fourier transform on Clifford multivector-valued functions (f : R-3 -> Cl-3,Cl-0). Third, we show a set of important properties of the Clifford Fourier transform on Cl-3,Cl-0 such as differentiation properties, and the Plancherel theorem. Finally, we apply the Clifford Fourier transform properties for proving an uncertainty principle for Cl-3,Cl-0 multivector functions.

引用

页码：41 / 61

页数：21