The existence of subspace wavelet sets
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摘要
Let H be a reducing subspace of L2(Rd), that is, a closed subspace of L2(Rd) with the property that f(Amt−ℓ)∈H for any f∈H, m∈Z and ℓ∈Zd, where A is a d×d expansive matrix. It is known that H is a reducing subspace if and only if there exists a measurable subset M of Rd such that AtM=M and F(H)=L2(Rd)·χM. Under some given conditions of M, it is known that there exist A-dilation subspace wavelet sets with respect to H. In this paper, we prove that this holds in general.
论文关键词:Frame,Wavelet,Frame wavelet,Frame wavelet set,Fourier transform
论文评审过程:Available online 9 April 2003.
论文官网地址:https://doi.org/10.1016/S0377-0427(02)00893-2