Abstract
Under study are sufficient sets in Frechet spaces of entire functions with uniform weighted estimates. We obtain general results on the a priori overflow of these sets and introduce the concept of their minimality. We also establish necessary and sufficient conditions for a sequence of points on the complex plane to be a minimal sufficient set for a weighted Frechet space. Applications are given to the problem of representation of holomorphic functions in a convex domain with certain growth near the boundary by exponential series.
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