Parameterization of Bivariate Nonseparable Orthogonal Symmetric Scaling Functions with Short Support

DOI：10.3770/j.issn:1000-341X.2010.04.008

 作者 单位 杨守志 汕头大学数学系,广东 汕头 515063 薛艳梅 汕头大学数学系,广东 汕头 515063

设 $I$ 是 $2\times 2$ 单位矩阵, $M$ 是 $2\times 2$ 伸缩矩阵,满足$M^2=2I$.首先建立伸缩因子为$M$和$2I$两种尺度函数之间的关系. 基于两者之间的关系,给出一类伸缩因子为$M$的紧支撑正交对称的二元不可分尺度函数的参数形式.最后给出一个相应的构造算例.

Let $I$ be the $2\times 2$ identity matrix, and $M$ a $2\times 2$ dilation matrix with $M^2=2I$. First, we present the correlation of the scaling functions with dilation matrix $M$ and $2I$. Then by relating the properties of scaling functions with dilation matrix $2I$ to the properties of scaling functions with dilation matrix $M$, we give a parameterization of a class of bivariate nonseparable orthogonal symmetric compactly supported scaling functions with dilation matrix $M$. Finally, a construction example of nonseparable orthogonal symmetric and compactly supported scaling functions is given.