Geodesic
Approximation of discrete functions and size of spectrum
Algebra i analiz, Tome 21 (2009) no. 6, pp. 227-240.

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Let $\Lambda\subset\mathbb R$ be a uniformly discrete sequence and $S\subset\mathbb R$ a compact set. It is proved that if there exists a bounded sequence of functions in the Paley–Wiener space $PW_S$ that approximates $\delta$-functions on $\Lambda$ with $l^2$-error $d$, then the measure of $S$ cannot be less than $2\pi(1-d^2)D^+(\Lambda)$. This estimate is sharp for every $d$. A similar estimate holds true when the norms of approximating functions have a moderate growth; the corresponding sharp growth restriction is found.
Keywords: Paley–Wiener space, Bernstein space, set of interpolation, approximation of discrete functions. 
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A. Olevskiǐ; A. Ulanovskiǐ. Approximation of discrete functions and size of spectrum. Algebra i analiz, Tome 21 (2009) no. 6, pp. 227-240. http://geodesic.mathdoc.fr/item/AA_2009_21_6_a7/

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