再生核空间中的微分算子样条小波  

WAVELET ANALYSIS OF DIFFERENTIAL OPERATOR SPLINE IN REPRODUCING KERNEL SPACE

作　　者：吴勃英[1] 崔明根[1] 

机构地区：[1]哈尔滨工业大学数学系,哈尔滨150001

出　　处：《高等学校计算数学学报》2000年第2期183-192,共10页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金资助项目 !( 1950 10 10 ;199710 2 0 )

摘　　要：This paper mainly discusses the wavelet theory for a non polynomial differntial operator spline in W 2(R) space, which is the further development of polynomial wavelet. Firstly, it gives the definition of wavelet analysis in W 2(R) space. Then it gives wavelet’s projection expression to several special properties in W 2(R) space. It also proves that the projection approximation function u j(x) is the interpolating function of u(x) in dense set {2 jk} k∈Z (j<0) . But the projection avoids calculating integral in inner products, so it is an ideal tool to approximate discrete function. Thus the results have an important meaning both in theory and method.This paper mainly discusses the wavelet theory for a non polynomial differntial operator spline in W 2(R) space, which is the further development of polynomial wavelet. Firstly, it gives the definition of wavelet analysis in W 2(R) space. Then it gives wavelet's projection expression to several special properties in W 2(R) space. It also proves that the projection approximation function u j(x) is the interpolating function of u(x) in dense set {2 jk} k∈Z (j<0) . But the projection avoids calculating integral in inner products, so it is an ideal tool to approximate discrete function. Thus the results have an important meaning both in theory and method.

关 键 词：再生核空间 微分算子样条 小波分析 插值逼近 

分 类 号：O241.3[理学—计算数学] O174.2[理学—数学]