伸缩因子为M的全正加细函数  

A Class of Totally Positive Refinable Function with Dilation Factor M

作　　者：杨守志[1] 朱天翔[1] 

机构地区：[1]汕头大学数学系,广东汕头515063

出　　处：《汕头大学学报（自然科学版）》2007年第4期46-52,59,共8页Journal of Shantou University：Natural Science Edition

基　　金：广东省自然科学基金资助项目(No:05008289;032038);广东省自然科学博士基金资助项目(No:04300917)

摘　　要：讨论伸缩因子为M,M≥2的全正加细函数的构造问题.研究它的精度、光滑性和对称性等性质,给出一类全正、对称、光滑的加细函数的显示构造方法,证明该类加细函数有很多性质与B-样条加细函数类似,可以通过卷积的方式增加加细函数的光滑性.The construction of a class of totally positive refinable function with dilation factor M is investigated, and its properties, such as accuracy, smoothness and symmetry, are discussed. An explicit way for constructing totally positive, symmetry and smoothness reflnable function is provided, and it is proved that many properties of this class of refinable function are similar to the cardinal B-spline. Hence its smoothness can be lifted using the method of convolution.

关 键 词：加细函数 伸缩因子 全正性 加细函数方程 

分 类 号：O174.2[理学—数学]