Geodesic
Minimal absolutely representing systems of exponential functions in spaces of analytic functions with given boundary smoothness
Vladikavkazskij matematičeskij žurnal, Tome 14 (2012) no. 3, pp. 13-30

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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. 
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     author = {A. V. Abanin and S. V. Petrov},
     title = {Minimal absolutely representing systems of exponential functions in spaces of analytic functions with given boundary smoothness},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
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     number = {3},
     year = {2012},
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     url = {http://geodesic.mathdoc.fr/item/VMJ_2012_14_3_a2/}
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A. V. Abanin; S. V. Petrov. Minimal absolutely representing systems of exponential functions in spaces of analytic functions with given boundary smoothness. Vladikavkazskij matematičeskij žurnal, Tome 14 (2012) no. 3, pp. 13-30. http://geodesic.mathdoc.fr/item/VMJ_2012_14_3_a2/