Frame-type families of translates

Details Frame-type families of translates Frame-type families of translates

2008-09-13

arxiv.org/abs/0809.2326v1

Mathematics

Classical Analysis and ODEs

10 pages

Scientific paper

We construct a uniformly discrete, and even sparse, sequence of real numbers $\Lambda=\{\lambda_n\}$ 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 $\sum c_n g(t-\lambda_n)$ 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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