Approximation of discrete functions and size of spectrum
Approximation of discrete functions and size of spectrum
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 PaleyâWiener space $PW_S$ that approximates $\delta$-functions on $\Lambda$ with $l^2$-error $d$, then the measure of $S$ cannot be less …