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

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。 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