Multivariate F-splines and Fractional Box Splines

doi:10.1007/s00041-009-9083-z

	Multivariate F-splines and Fractional Box Splines
	Xu, Zhiqiang
	2009-10-01
发表期刊	JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
ISSN	1069-5869
卷号	15 期号:5 页码:723-738
摘要	We introduce multivariate F-splines, including multivariate F-truncated powers T-f (.\|M) and F-box splines B-f (.\|M). The classical multivariate polynomial splines and multivariate E-splines can be considered as a special case of multivariate F-splines. We document the main properties of T-f (.\|M) and B-f (.\|M). Using T-f (.\|M), we extend fractional B-splines to fractional box splines and show that these functions satisfy most of the properties of the traditional box splines. Our work unifies and generalizes results due to Dahmen-Micchelli, de Boor-Hollig, Ron and Unser-Blu, and also presents a new tool for computing the integration over polytopes.
关键词	Box splines Multivariate truncated powers Fractional B-splines
DOI	10.1007/s00041-009-9083-z
语种	英语
资助项目	National Natural Science Foundation of China[10871196] ; Alexander von Humboldt Foundation
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000272034700008
出版者	SPRINGER BIRKHAUSER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/8070
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	Chinese Acad Sci, LESC, Inst Comp Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Xu, Zhiqiang. Multivariate F-splines and Fractional Box Splines[J]. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS,2009,15(5):723-738.
APA	Xu, Zhiqiang.(2009).Multivariate F-splines and Fractional Box Splines.JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS,15(5),723-738.
MLA	Xu, Zhiqiang."Multivariate F-splines and Fractional Box Splines".JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS 15.5(2009):723-738.