关于非齐次细分方程的一个注记(英文)

A Note on Nonhomogeneous Refinement Equation

非齐次细分方程在区间上小波构造中用于边界小波的构造，同时它还用于向量小波构造等方面．本文讨论了非齐次细分方程在Lp（R）（1≤p≤∞）中解的存在性和正则性，特别地，用迹类算子的谱半径给出了解的Sobolev指数的一个下界估计，同时还给出了一些例子来说明这些一般性的结论．

Nonhomogeneous refinement equations are used in the construction of boundarywavelets in the construction Of interVal wavelets, and used in the construction of multiwavelets. Inthis paper, the existence and the regularity of the solutions to nonhomogeneous refinement equationsin LP(R)(1 5 p 5 co) are discussed, especially' an estimate Of the lower bound of the Sobolevexponent of the solutions is given. Some examples are provided to illustrate the general theory.