一类多维连续小波逆变换的逐点收敛性  

Pointwise Convergence of a Class of Multi-dimensional Continuous Wavelet Inverse Transform

作　　者：杨姗 江慎铭[1] YANG Shan;JIANG Shen-ming(School of Mathematics and Information Science,Nanchang Hangkong University,Nanchang 330063,China)

机构地区：[1]南昌航空大学数学与信息科学学院,江西南昌330063

出　　处：《南昌航空大学学报（自然科学版）》2022年第4期43-48,共6页Journal of Nanchang Hangkong University(Natural Sciences)

基　　金：南昌航空大学博士启动基金(EA201807304)。

摘　　要：研究了多维连续小波逆变换的逐点收敛性。首先引入一类多维连续小波,这类多维连续小波变换具有高频时,小移动,低频时,大移动的特点;其次讨论了这类多维连续小波的逐点收敛性,给出了这类多维连续小波逆变换逐点收敛成立的一个充分条件。In this work, a pointwise convergence of multi-dimensional continuous wavelet inverse transform was studied. Firstly, a kind of multi-dimensional continuous wavelet transform was introduced, which features small shift at high frequency and large shift at low frequency. Secondly, the pointwise converfence of muti-dimensional continuous wavelet was discussed, and a sufficient condition for the pointwise convergence of this multi-dimensional continuous wavelet inverse transform was given.

关 键 词：多维连续小波 逐点收敛 小波逆变换 

分 类 号：O174.2[理学—数学]