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Minimal absolutely representing systems of exponential functions in spaces of analytic functions with given boundary smoothness
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
Language: Russian Download the full text
For citation: Abanin A. V.,† Petrov S. V. Minimal absolutely representing systems of exponential functions in spaces of analytic functions with given boundary smoothness. Vladikavkazskij matematicheskij zhurnal [Vladikavkaz Math. J.], 2012, vol. 14, no. 3, pp.13-30. DOI 10.23671/VNC.2012.14.10966
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