Title

The Existence Of Subspace Wavelet Sets

Keywords

Fourier transform; Frame; Frame wavelet; Frame wavelet set; Wavelet

Abstract

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.

Publication Date

6-1-2003

Publication Title

Journal of Computational and Applied Mathematics

Volume

155

Issue

1

Number of Pages

83-90

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/S0377-0427(02)00893-2

Socpus ID

0037980391 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0037980391

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