  The paper discusses sharp sufficient conditions for interpolation and
sampling for functions of n variables with convex spectrum. When n=1, the
classical theorems of Ingham and Beurling state that the critical values in the
estimates from above (from below) for the distances between interpolation
(sampling) nodes are the same. This is no longer true for n>1. While the
critical value for sampling sets remains constant, the one for interpolation
grows linearly with the dimension.
