用符号刻划多变量加细函数向量的精度

Characterising the Accuracy of Multivariable Refinable Functions via the Symbol Function

假定ｆ（ｘ）＝（ｆ１（ｘ），…，ｆｒ（ｘ））Ｔ，ｘ∈Ｒｄ是一个满足矩阵加细方程ｆ（ｘ）＝的向量函数，其中Ａ是Ｚｄ中的有限集，ｃｋ是ｒ×ｒ，矩阵．由小波分析的多尺度分析方法可知，加细向量ｆ的性质需要由符号叫ｍ（ξ）来反映．本文，我们给出了用符号来刻划多变量加细向量ｆ具有Ｐ阶精度的充分必要条件．

Suppose that f(x) = (f1(x),... ,fr(x))T, a ? Rd is a vector-valued function satisfying the refinement equation f(x) with finite set of Zd and some r × r matricex Ck. The requirements for f to have accuracy p are given in terms of the symbol function m(ξ).