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arXiv · 0809.2326

Frame-type families of translates

Shahaf Nitzan-Hahamov·Alexander Olevskii
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Abstract

We construct a uniformly discrete, and even sparse, sequence of real numbers $Λ=\{λ_n\}$ and a function g in $L^2(R)$, such that for every q>2, every function f in $L^2(R)$ can be approximated with arbitrary small error by a linear combination $\sum c_n g(t-λ_n)$ with an $l_q$ estimate of the coefficients: \|\{c_n\}\|_{l_q}\leq C(q)\|f\|. This can not be done for q=2, according to [2].

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Shahaf Nitzan-Hahamov, Alexander Olevskii. 2008-09-13. Frame-type families of translates. https://arxiv.org/abs/0809.2326

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