四元数值可允许小波变换及Weyl变换
Quaternion-Valued Admissible Wavelet Transform and Weyl Transform

作者: 刘 茵 :北京师范大学数学科学学院,数学与复杂系统教育部重点实验室,北京 ; 赵纪满 :北京师范大学数学科学学院,数学与复杂系统教育部重点实验室,北京;

关键词: 四元数可允许小波Weyl变换Quaternion Admissible Wavelet Weyl Transform

摘要:
本文研究了一种与特殊的Fourier变换相关的四元数值可允许小波变换,给出了此类可允许小波变换的一些性质,然后定义了与其相关的Weyl变换,证明当1≤p≤2时,Weyl算子Wσ是有界的。

Abstract: In this paper, we study one kind of quaternion-valued admissible wavelet transform related to a special Fourier transform. We present some properties of this kind of the admissible wavelet transform. Then, we define the Weyl transform associated with the quaternion-valued admissible wavelet transform, and prove that the Weyl operators Wσ are bounded when 1≤p≤2

文章引用: 刘 茵 , 赵纪满 (2015) 四元数值可允许小波变换及Weyl变换。 理论数学, 5, 219-226. doi: 10.12677/PM.2015.55031

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