Abstract
Suppose that is a convex domain in , the space of functions holomorphic in endowed with the topology of uniform convergence on compact sets, and a closed subspace in invariant with respect to the operator of differentiation and admitting spectral synthesis.In this paper it is shown that an arbitrary function may be uniformly approximated by linear combinations of exponential monomials from , not only within but also in the whole domain of existence of , if the annihilator submodule of contains an entire function of exponential type which on a sequence of circles , as , admits the estimate (, ).Bibliography: 10 titles.
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