Classification of refinable splines

被引：17

作者：

Dai, XR ^{[1
]}

Feng, DJ

Wang, Y

机构：

[1] Zhejiang Univ Technol, Dept Appl Math, Hangzhou 310014, Peoples R China

[2] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

[3] Tsing Hua Univ, Dept Math Sci, Beijing 100084, Peoples R China

[4] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China

来源：

CONSTRUCTIVE APPROXIMATION | 2006年 / 24卷 / 02期

关键词：

spline; refinable spline; quasi-trigonometric polynomial; Weierstrass factorization theorem;

D O I：

10.1007/s00365-005-0622-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：187 / 200

页数：14