再生核Hilbert空间中的采样定理  

Sampling Theorem in A Reproducing Kernel Hilbert Space

作　　者：王旭[1] 邓彩霞[1] 朱建立[1] 

机构地区：[1]哈尔滨理工大学应用科学学院,黑龙江哈尔滨150080

出　　处：《哈尔滨理工大学学报》2008年第6期66-68,共3页Journal of Harbin University of Science and Technology

摘　　要：首先从线性变换的角度出发,结合再生核Hilbert空间中再生核函数的特殊性质,利用再生核函数建立了再生核Hilbert空间中函数的采样定理,并给出了误差估计,为再生核Hilbert空间中的数值逼近问题提供了理论基础.In this paper, a sampling expansion formula which bases are defined as reproducing kernel function is given by using some special properties of reproducing kernel functions in the Hilbert space at first, then a sampiing formula of reproducing kernel function in Hilbert space are derived by using reproducing kernel functions. Meanwhile estimation of error is given. The results play a fundamental role in the problem of numerical approximation and it also convenient to numerical calculations.

关 键 词：再生核 再生核HILBERT空间 采样定理 

分 类 号：O29[理学—应用数学]