离散小波系统的加权密度
The Weighted Density of Discrete Wavelet Systems
DOI: 10.12677/PM.2022.128142, PDF,    科研立项经费支持
作者: 杨 姗, 江慎铭*：南昌航空大学数学与信息科学学院，江西 南昌
关键词: 离散小波系统；过采样小波系统；加权密度；Discrete Wavelet Systems； Oversampled Wavelet Systems； Weighted Density
摘要: 引入了一类新的连续小波变换，该变换的缩放因子指数大于0，其弱收敛意义上的重构公式被给出。在此基础上，相应于此类连续小波变换的离散小波系统、过采样离散仿射小波系统及它们的仿射Beurling密度、加权仿射Beurling密度定义也被给出。验证了新给出的离散小波系统具有一致仿射Beurling密度，新给出的过采样离散仿射小波系统具有一致加权仿射Beurling密度，并且两者的值相等。
Abstract: A new class of continuous wavelet transform is introduced, whose scaling factor index is greater than 0, and its reconstruction formula in the sense of weak convergence is given. On this basis, the definitions of discrete wavelet systems; oversampled discrete affine wavelet systems and their af-fine Beurling density, and weighted affine Beurling density corresponding to this kind of continuous wavelet transform are also given. It is verified that the new discrete affine wavelet system has uni-form affine Beurling density, and the new oversampled discrete affine wavelet system has uniformly weighted affine Beurling density, and the values of the two are equal.
文章引用：杨姗, 江慎铭. 离散小波系统的加权密度[J]. 理论数学, 2022, 12(8): 1296-1304. https://doi.org/10.12677/PM.2022.128142

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