Upper Bounds For The Concentration of Bandlimited Functions on Sparse Sets.

Estimates are given for the concentration of bandlimited functions in L sub p (E) for sets E whose indicator functions satisfy a moving average constraint. In the case of sparse sets the concentration is shown to be approximately equal to the concentration on point sets {lambda sub n}, where the lambda sub n satisfy a separation constraint, lambda sub (n+1) - lambda sub (n) >= T . The maximum concentration on such point sets is found for all p >=1 in case T is a Nyquist interval, and for certain other T in case p = 1 and p = 2 .