Sampling analysis in the complex reproducing kernel Hilbert space

被引：4
|
作者：
Li, Bing-Zhao [1 ,2 ]
Ji, Qing-Hua [1 ]
机构：
[1] Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China
[2] Beijing Key Lab Fract Signals & Syst, Beijing 100081, Peoples R China
来源：
EUROPEAN JOURNAL OF APPLIED MATHEMATICS | 2015年 / 26卷
基金：
中国国家自然科学基金;
关键词：
reproducing kernel Hilbert space (RKHS); sampling theorem; linear canonical transform (LCT); LINEAR CANONICAL TRANSFORM; BAND-LIMITED SIGNALS; FRACTIONAL FOURIER-TRANSFORM; SPLINE SUBSPACES; RECONSTRUCTION; CONVOLUTION; THEOREMS;
D O I：
10.1017/S0956792514000357
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider and analyse sampling theories in the reproducing kernel Hilbert space (RKHS) in this paper. The reconstruction of a function in an RKHS from a given set of sampling points and the reproducing kernel of the RKHS is discussed. Firstly, we analyse and give the optimal approximation of any function belonging to the RKHS in detail. Then, a necessary and sufficient condition to perfectly reconstruct the function in the corresponding RKHS of complex-valued functions is investigated. Based on the derived results, another proof of the sampling theorem in the linear canonical transform (LCT) domain is given. Finally, the optimal approximation of any band-limited function in the LCT domain from infinite sampling points is also analysed and discussed.
引用
收藏
页码：109 / 120
页数：12
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