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Vladikavkazskii Matematicheskii Zhurnal, 2011, Volume 13, Number 1, Pages 44–58
(Mi vmj375)
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This article is cited in 4 scientific papers (total in 4 papers)
On the expansions of analytic functions on convex locally closed sets in exponential series
S. N. Melikhovab, S. Mommc a Southern Federal University, Department of Mathematics, Mechanics and Computer Science, RUSSIA, Rostov on Don
b Southern Mathematical Institute, Vladikavkaz Science Center of the RAS, Complex Analysis Laboratory, RUSSIA, Vladikavkaz
c Mathematisches Institut Heinrich-Heine Universität, Düsseldorf, GERMANY, Düsseldorf
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.
Key words:
locally closed set, analytic functions, exponential series, continuous linear right inverse.
Received: 01.02.2010
Citation:
S. N. Melikhov, S. Momm, “On the expansions of analytic functions on convex locally closed sets in exponential series”, Vladikavkaz. Mat. Zh., 13:1 (2011), 44–58
Linking options:
https://www.mathnet.ru/eng/vmj375 https://www.mathnet.ru/eng/vmj/v13/i1/p44
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