多小波子空间上的单小波表示

Representation for Multiwavelets Subspaces by the Uni-Wavelet

本文在较弱的条件下,建立了2重多小波子空间与单小波子空间的关系.即由2重多小波构造出单小波.一方面,这种单小波的平移伸缩与2重多小波的平移伸缩生成的子空间是完全相同的;另一方面,它具有插值性.因此通过构造出的单小波建立了多小波子空间上的Shannon型采样定理.

Under weak hypotheses, we establish the relation between multiwavelets subspaces with multiplicity 2 and uni-wavelet subspaces, i.e., the uni-wavelet is constructed by multiwavelets with multiplicity 2. On the one hand, the subspace generated by translates and dilations of the uni-wavelet is the same as the subspace generated by multiwavelets with multiplicity 2; on the other hand, the uni-wavelet also possesses the interpolatory property. Based on uni-wavelet generated by our method, the Shan-non'type sampling theorem on the multiwavelets subspace is presented.