Wavelet shrinkage estimators of Calderon-Zygmund operators with odd kernels

被引：0
作者：
Chen Heng [1 ]
Wu JiTao [1 ]
机构：
[1] Beijing Univ Aeronaut & Astronaut, Dept Math, Beijing 100191, Peoples R China
来源：
SCIENCE CHINA-MATHEMATICS | 2014年 / 57卷 / 09期
基金：
中国国家自然科学基金;
关键词：
wavelets shrinkage; singular integral operator; non-standard form; maximal operator; COMPACTLY SUPPORTED WAVELETS; DIFFERENTIAL-OPERATORS; CONVERGENCE; BASES;
D O I：
10.1007/s11425-013-4724-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Wavelet shrinkage is a strategy to obtain a nonlinear approximation to a given function f and is widely used in data compression, signal processing and statistics, etc. For Calderon-Zygmund operators T, it is interesting to construct estimator of Tf, based on wavelet shrinkage estimator of f. With the help of a representation of operators on wavelets, due to Beylkin et al., an estimator of Tf is presented in this paper. The almost everywhere convergence and norm convergence of the proposed estimators are established.
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页码：1983 / 1991
页数：9
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