On the expansions of analytic functions on convex locally closed sets in exponential series

Melikhov S. N. , Momm S.
Vladikavkaz Mathematical Journal 2011. Vol. 13. Issue 1.

Abstract:
Let \(Q\) be a bounded, convex, locally closed subset of \({\mathbb C}^N\) with nonempty interior. For \(N>1\) sufficient conditions are obtained that an operator of the representation of analytic functions on \(Q\) by exponential series has a continuous linear right inverse. For \(N=1\) the criterions for the existence of a continuous linear right inverse for the representation operator are proved.

Keywords: locally closed set, analytic functions, exponential series, continuous linear right inverse.

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