studyonthegeneratorfoftheoperatorsinandit

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	studyonthegeneratorfoftheoperatorsinandit
	Chen Hanlin
	2010
发表期刊	sciencechinamathematics
ISSN	1674-7283
卷号	53 期号:10 页码:2589
摘要	Define two operators In and It,the inner product operator In(g)(x):=∑_(j ∈Zs)(g,f(·-j))f(x-j) and the interpolation operator It(g)(x):=∑_(j ∈Zs)g(j)f(x-j),where f belongs to some space and integer s≥1. We call f the generator of the operators In and I_t.It is well known that there are many results on operators I_n and I_t.But there remain some important problems to be further explored.For application we first need to find the available generators(that can recover polynomials as I_t(p)=p or I_n(p)=p,p∈Π_(m-1))for constructing the relative operators.In this paper,we focus on the available generator in the class of spline functions.We shall see that not all spline functions can be used to construct available generators.Fortunately,we do find a spline function in S,of degree m-1,where m is even and S is a class of splines.But for odd m the problem is still open.Results on spline functions in this paper are new
语种	英语
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/40949
专题	中国科学院数学与系统科学研究院
作者单位	中国科学院数学与系统科学研究院
推荐引用方式 GB/T 7714	Chen Hanlin. studyonthegeneratorfoftheoperatorsinandit[J]. sciencechinamathematics,2010,53(10):2589.
APA	Chen Hanlin.(2010).studyonthegeneratorfoftheoperatorsinandit.sciencechinamathematics,53(10),2589.
MLA	Chen Hanlin."studyonthegeneratorfoftheoperatorsinandit".sciencechinamathematics 53.10(2010):2589.