Convergence of Riemannian sums of inverse wavelet transforms

被引：2

作者：

Sun XuDong ^{[1
]}

Sun WenChang ^{[1
]}

机构：

[1] Nankai Univ, Dept Math & LPMC, Tianjin 300071, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2011年 / 54卷 / 04期

基金：

中国国家自然科学基金;

关键词：

wavelet frames; wavelet transforms; Riemannian sum; FRAMES;

D O I：

10.1007/s11425-011-4174-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the approximation of the inverse wavelet transform using Riemannian sums. We show that when the Fourier transforms of wavelet functions satisfy some moderate decay condition, the Riemannian sums converge to the function to be reconstructed as the sampling density tends to infinity. We also study the convergence of the operators introduced by the Riemannian sums. Our result improves some known ones.

引用

页码：681 / 698

页数：18

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