Study on the generator f of the operators I-n and I-t

doi:10.1007/s11425-010-4065-9

CSpace

	Study on the generator f of the operators I-n and I-t
	Chen HanLin
	2010-10-01
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	53 期号:10 页码:2589-2603
摘要	Define two operators I-n and I-t, the inner product operator I-n(g)(x) = Sigma(j is an element of zs)(g, f(- j))f(x - j) and the interpolation operator I-t(g)(x) = Sigma(j epsilon zs)g(j)f(x - j), where f belongs to some space and integer s >= 1 We call f the generator of the operators I-n 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 is an element of Pi(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
关键词	generator available generator inner product operator spline interpolation operator two-closed refinable
DOI	10.1007/s11425-010-4065-9
语种	英语
资助项目	National Natural Science Foundation of China[10671062] ; National Natural Science Foundation of China[60972126]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000283671200002
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/9312
专题	中国科学院数学与系统科学研究院
通讯作者	Chen HanLin
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Chen HanLin. Study on the generator f of the operators I-n and I-t[J]. SCIENCE CHINA-MATHEMATICS,2010,53(10):2589-2603.
APA	Chen HanLin.(2010).Study on the generator f of the operators I-n and I-t.SCIENCE CHINA-MATHEMATICS,53(10),2589-2603.
MLA	Chen HanLin."Study on the generator f of the operators I-n and I-t".SCIENCE CHINA-MATHEMATICS 53.10(2010):2589-2603.