Abstract
This article deals with the operator of multiplication by an entire function with indicator when the order is . This operator acts from to , where is a sequence of indicators, with the standard space of entire functions. It is assumed that the spaces are isomorphic, with respect to a transformation of Borel type, to spaces of functions analytic on many-sheeted closed sets. A criterion is found for the range of to be closed. It is used to derive, in particular, a criterion for an operator of convolution type in a union of -convex domains to be an epimorphism, along with known results about convolution operators and operators of convolution type. The conditions connect the directions of non-completely-regular growth of and of accumulation of its zeros with geometric characteristics of .Bibliography: 26 titles.
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