调和分析与小波研究中的逼近论方法  

Methods of approximation theory in research of harmonic analysis and wavelets

作　　者：施咸亮 陈洋 Xianliang Shi;Yang Chen

机构地区：[1]湖南师范大学数学与统计学院高性能计算与随机信息处理省部共建教育部重点实验室,长沙410081

出　　处：《中国科学：数学》2018年第10期1443-1456,共14页Scientia Sinica：Mathematica

基　　金：湖南省自然科学基金(批准号:2018JJ3329);湖南师范大学博士科研启动金(批准号:5311203258)资助项目

摘　　要：本文介绍了函数逼近论对调和分析与小波研究的应用.本文从Korovkin定理开始,介绍了试验函数法对小波研究的应用、Jackson算子逼近对奇异积分算子有界性研究的应用、正则线性求和与逼近对边界探测研究以及Fourier逆变换计算的应用、以及稀疏数据反构函数的新结果.In this paper, we give a brief introduction about applications of approxiamtion theory of functions in harmonic analysis and wavelet research. We start from Korovkin＇s theorem to introduce applications of test functions in wavelet research. Then we present boundedness of singular integrals by using Jackson approximation.In addition, applications of regular linear summation and approximation in edge detection and inverse Fourier transform are stated. We also introduce some new results in signal reconstruction by sparse data.

关 键 词：函数逼近论 调和分析 小波 

分 类 号：O174.2[理学—数学]