多个尺度函数产生的多分辨率分析(英文)

Multiresolution Generated by Several Scaling Functions

本文考虑一般细分方程φｉ（ｘ）＝Σ１ｊＮΣｋ∈Ｚｃｉｊ（ｋ）φｊ（２ｘ－ｋ），１ｉＮ解的存在性，正则性和稳定性。

Existence and regularity of solutions of the refinement equation  φ i(x)=Σ 1jN Σ k∈Z c ij (k)φ j(2x-k), 1iN  and conditions under which {φ i} 1iN generate a multiresolution are considered in this paper. Examples are constructed to illustrate the theory.