On coefficients of exponential series for analytic functions of polynomial growth

Melikhov S. N. , Varziev V. A.
Vladikavkaz Mathematical Journal 2011. Vol. 13. Issue 4.

Abstract:
In this article a criterion is obtained that the operator of the representation of analytic functions on a bounded convex domain \(G\) of polynomial growth near the boundary of $G$ by exponential series, exponents of which are zeroes of a special entire function, has a continuous linear right inverse.

Keywords: exponential series, analytic functions of polynomial growth, representation operator, continuous linear right inverse.

The sole copyright holder of the published work is the Founder of the Vladikavkaz Mathematical Journal. The terms of use of this work are governed by an open license (Creative Commons Attribution-NonCommercial 4.0 International). The use of metadata of the scientific article, including the title, abstract, author information, references, identifiers, and other bibliographic description elements for subsequent unrestricted use, is carried out under the terms of the CC BY or CC0 open licenses.