The Existence Of Subspace Wavelet Sets
Fourier transform; Frame; Frame wavelet; Frame wavelet set; Wavelet
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. © 2003 Elsevier Science B.V. All rights reserved.
Journal of Computational and Applied Mathematics
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Dai, X.; Diao, Y.; and Gu, Q., "The Existence Of Subspace Wavelet Sets" (2003). Scopus Export 2000s. 1738.