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DOI: 10.23671/VNC.2011.1.11350

# 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.