$L^2-$interpolation with error and size of spectra
  Given a compact set $S$ and a uniformly discrete sequence $\La$, we show that "approximate interpolation" of delta--functions on $\La$ by a bounded sequence of $L^2-$functions with spectra in $S$ implies an estimate on measure of $S$ through the density of $\La$. 
Alexander Olevskii and Alexander Ulanovskii