【摘要】 细致地讨论了在Hilbert空间中的框架与Riesz基的关系。设{Vj}是L2(R)的一个多分辨分析,Wj Vj=Vj+1,母小波ψ(x)∈W0使得{ψjk(x)=2j2ψ(2jx-k)∶k∈Z}是Wj的Riesz基。将证明{ψj,k∶j,k∈Z}是整个空间L2(R)的Riesz基并且存在唯一的对偶小波ψ使得ψ与ψ满足双正交条件。更多还原

【Abstract】 <Abstrcat> We will discuss meticulously the relationship between frame and Riesz basis in Hilbert space.Let｛V_j｝ be a multiresolution analysis of L²（R）,and W_jV_j=V_j+1,the mother wavelet ψ（x）∈W₀ which makes ψ_j,k=2^j2ψ（2^jx-k）:k∈Z is a Riesz basis of W_j.We will show that ｛ψ_j,k:j,k∈Z｝ is a Riesz basis in the whole space L²（R） and there is the only dual wavelet such that ψ and satisfy the biorthogonal condition.更多还原