多分辨分析中尺度函数的一个注记

ON THE THREE KINDS OF SCALE FUNCTIONS IN THE MULTIRESOLUTION ANALYSIS

在本文中除了通常的多分辨分析的尺度方程以外 ,我们又给出了两类新的所谓的广义尺度方程 .第一类是用积分方程表示的 ,第二类是用微分方程表示的 .在前一种情况下 ,我们给出了用尺度方程的解去构造多分辨分析的方法 .在后一种情况下 ,我们指出了除了特殊情况以外 ,用微分方程的解是不能构造多分辨分析的 .

In this paper, we give two new kinds of so-called generalized scale equations besides the ordinary scale equation of multiresolution analysis. The first kinds is repressented by the integral equation, and the second kind is expressed by the differential equation. As for the former, we give a method of forming a multiresolution analysis with the solution of the scale equation, and for the later, we show that the solution of the differential equation can't form a multiresolution analysis except for the special casses.