基于L^2(0,1)~2空间Riesz基的二维小波子空间采样定理

Riesz bases in L^2(0,1)~2 related to sampling in 2-dimenional wavelet subspace

证明了在二维小波子空间上存在一种傅立叶对偶算法,即由φ生成的二维小波子空间V0是L2(0,1)2到L2(R2)的有界可逆线性算子T的值域.通过T扩展L2((0,1)2)空间的Riesz基,进而得到V0∈L2(R2)空间的采样定理.

It is proved that there exists an analogue of the Fourier duality technique in wavelet subspace. Any wavelet subspace V0 with a generator φ is the range space of a bounded one-to-one linear operator T between L^2 （0,1）^2 and L^2 （ R^2 ）. Thus, sampling formulae in V0 are obtained by transforming, via T, expansions in L^2 （0,1 ）^2 with respect to some appropriate Riesz bases.