Universal Sampling and Interpolation of Band-Limited Signals

Abstract.

We ask if there exist discrete “universal” sets $\bigwedge$ of given finite density such that every signal f with bounded spectrum of small measure can be recovered from the samples $f(\lambda),\,\lambda \in \bigwedge$. We prove that uniqueness in this problem can be achieved in general situation. On the other hand, for stable reconstruction it is crucial whether the spectrum is compact or dense.