四元数值可允许小波变换及Weyl变换.pdfVIP

Pure Mathematics 理论数学, 2015, 5(5), 219-226 Published Online September 2015 in Hans. /journal/pm /10.12677/pm.2015.55031 Quaternion-Valued Admissible Wavelet Transform and Weyl Transform Yin Liu, Jiman Zhao* Key Laboratory of Mathematics and Complex Systems, Ministry of Education, School of Mathematical Sciences, Beijing Normal University, Beijing * Email: lylight@, jzhao@ th nd th Received: Aug. 30 , 2015; accepted: Sep. 22 , 2015; published: Sep. 25 , 2015 Copyright © 2015 by authors and Hans Publishers Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). /licenses/by/4.0/ 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 W are bounded when 1 ≤p ≤2 . σ Keywords Quaternion, Admissible Wavelet, Weyl Transform 四元数值可允许小波变换及Weyl变换 刘 茵，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 * Email: lylight@, jzhao@ 收稿日期：2015年8月30 日；录用日期：2015年9月22 日；发布日期：2015年9月25 日 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 *通讯作者。 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. /10.12677/pm.2015.55031 刘茵，赵纪满 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 是有界的。 W