Minimal absolutely representing systems of exponential functions in spaces of analytic functions with given boundary smoothness

Abanin, A. V. , Petrov S. V.
Vladikavkaz Mathematical Journal 2012. Vol. 14. Issue 3.

Abstract:
We consider spaces of functions holomorphic in a convex domain which are infinitely differentiable up to the boundary and have certain estimates of all derivatives. Some necessary and sufficient conditions are obtained for a minimal system of exponential functions to be an absolutely representing system in the spaces which are generated by a single weight. Relying on these results, we prove that absolutely representing systems of exponentials do not have the stability property under the passage to the limit over domains.

Keywords: absolutely representing systems, spaces of analytic functions, boundary smoothness

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