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	Classification of refinable splines
	Dai, XR ; Feng, DJ ; Wang, Y
	2010-05-06 ; 2010-05-06
关键词	spline refinable spline quasi-trigonometric polynomial Weierstrass factorization theorem BERNOULLI CONVOLUTIONS SMOOTHNESS FAMILY Mathematics
中文摘要	A refinable spline is a compactly supported refinable function that is piecewise polynomial. Refinable splines, such as the well-known B-splines, play a key role in computer aided geometric design. So far all studies on refinable splines have focused on positive integer dilations and integer translations, and under this setting a rather complete classification was obtained in [12]. However, refinable splines do not have to have integer dilations and integer translations. The classification of refinable splines with noninteger dilations and arbitrary translations is studied in this paper. We classify completely all refinable splines with integer translations and arbitrary dilations. Our study involves techniques from number theory and complex analysis.
语种	英语 ; 英语
出版者	SPRINGER ; NEW YORK ; 233 SPRING STREET, NEW YORK, NY 10013 USA
内容类型	期刊论文
源URL	[http://hdl.handle.net/123456789/14203]
专题	清华大学
推荐引用方式 GB/T 7714	Dai, XR,Feng, DJ,Wang, Y. Classification of refinable splines[J],2010, 2010.
APA	Dai, XR,Feng, DJ,&Wang, Y.(2010).Classification of refinable splines..
MLA	Dai, XR,et al."Classification of refinable splines".(2010).

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