The Uncertainty Principle for the Two-Sided Quaternion Fourier Transform

被引：38
作者：
El Haoui, Youssef [1 ]
Fahlaoui, Said [1 ]
机构：
[1] Univ Moulay Ismail, Fac Sci, Dept Math & Comp Sci, Equipe Anal Harmon & Probabilites, BP 11201 Zitoune, Meknes, Morocco
来源：
MEDITERRANEAN JOURNAL OF MATHEMATICS | 2017年 / 14卷 / 06期
关键词：
Quaternion Fourier transform; Hardy's theorem; Uncertainty principle;
D O I：
10.1007/s00009-017-1024-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we provide the Heisenberg's inequality and the Hardy's theorem for the two-sided quaternion Fourier transform.
引用
收藏
页数：11
相关论文
共 12 条
[1]  
Bulow T, 1999, THESIS
[2]   Pitt's inequality and the uncertainty principle associated with the quaternion Fourier transform [J].
Chen, Li-Ping ;
Kou, Kit Ian ;
Liu, Ming-Sheng .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 423 (01) :681-700
[3]  
Christensen J. G, 2003, THESIS
[4]  
De Bie H., 2012, PROC AGACSE
[5]  
Eckhard M., 2013, ARXIV13061023V1MATHR
[6]  
ELL TA, 1993, PROCEEDINGS OF THE 32ND IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-4, P1830, DOI 10.1109/CDC.1993.325510
[7]  
Hardy GH., 1933, J. London Math. Soc, V8, P227, DOI [DOI 10.1112/JLMS/S1-8.3.227, 10.1112/jlms/s1-8.3.227]
[8]   Efficient implementation of quaternion Fourier transform, convolution, and correlation by 2-D complex FFT [J].
Pei, SC ;
Ding, JJ ;
Chang, JH .
IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2001, 49 (11) :2783-2797
[9]  
PIERCE LB, 2001, HARDY FUNCTIONS
[10]   An analogue of Hardy's theorem for very rapidly decreasing functions on semi-simple Lie groups [J].
Sitaram, A ;
Sundari, M .
PACIFIC JOURNAL OF MATHEMATICS, 1997, 177 (01) :187-200
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