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$ n\times$ oversampling preserves any tight affine frame for odd $ n$


Authors: Charles K. Chui and Xian Liang Shi
Journal: Proc. Amer. Math. Soc. 121 (1994), 511-517
MSC: Primary 42C15
DOI: https://doi.org/10.1090/S0002-9939-1994-1182699-5
MathSciNet review: 1182699
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Abstract: If $ \psi $ generates an affine frame $ {\psi _{j,k}}(x) = {2^{j/2}}\psi ({2^j}x - k),j,k \in \mathbb{Z}$, of $ {L^2}(\mathbb{R})$, we prove that $ \{ {n^{ - 1/2}}{\psi _{j,k/n}}\} $ is also an affine frame of $ {L^2}(\mathbb{R})$ with the same frame bounds for any positive odd integer n. This establishes the result stated as the title of this paper. A counterexample of this statement for $ n = 2$ is also given.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1182699-5
Keywords: Frames, frame bounds, wavelets, oversampling, recovery from wavelet transforms
Article copyright: © Copyright 1994 American Mathematical Society

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