Refinement equations and spline functions

doi:10.1007/s10444-008-9079-2

	Refinement equations and spline functions
	Dubickas, Arturas 2,3; Xu, Zhiqiang1
	2010
发表期刊	ADVANCES IN COMPUTATIONAL MATHEMATICS
ISSN	1019-7168
卷号	32 期号:1 页码:1-23
摘要	In this paper, we exploit the relation between the regularity of refinable functions with non-integer dilations and the distribution of powers of a fixed number modulo 1, and show the nonexistence of a non-trivial C (aaEuro parts per thousand) solution of the refinement equation with non-integer dilations. Using this, we extend the results on the refinable splines with non-integer dilations and construct a counterexample to some conjecture concerning the refinable splines with non-integer dilations. Finally, we study the box splines satisfying the refinement equation with non-integer dilation and translations. Our study involves techniques from number theory and harmonic analysis.
关键词	Refinement equation Multivariate spline Fourier transform Distribution modulo 1
DOI	10.1007/s10444-008-9079-2
语种	英语
资助项目	Lithuanian Foundation of Studies and Science ; National Natural Science Foundation of China[10401021]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000272901600001
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/11045
专题	计算数学与科学工程计算研究所
通讯作者	Xu, Zhiqiang
作者单位	1.Chinese Acad Sci, Inst Computat Math & Sci & Engn Comp, Acad Math & Syst Sci, Beijing 100080, Peoples R China 2.Vilnius State Univ, Dept Math & Informat, LT-03225 Vilnius, Lithuania 3.Inst Math & Informat, LT-08663 Vilnius, Lithuania
推荐引用方式 GB/T 7714	Dubickas, Arturas,Xu, Zhiqiang. Refinement equations and spline functions[J]. ADVANCES IN COMPUTATIONAL MATHEMATICS,2010,32(1):1-23.
APA	Dubickas, Arturas,&Xu, Zhiqiang.(2010).Refinement equations and spline functions.ADVANCES IN COMPUTATIONAL MATHEMATICS,32(1),1-23.
MLA	Dubickas, Arturas,et al."Refinement equations and spline functions".ADVANCES IN COMPUTATIONAL MATHEMATICS 32.1(2010):1-23.