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Sufficient sets in weighted Fréchet spaces of entire functions

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Abstract

Under study are sufficient sets in Fréchet spaces of entire functions with uniform weighted estimates. We obtain general results on the a priori overflow of these sets and introduce the concept of their minimality. We also establish necessary and sufficient conditions for a sequence of points on the complex plane to be a minimal sufficient set for a weighted Fréchet space. Applications are given to the problem of representation of holomorphic functions in a convex domain with certain growth near the boundary by exponential series.

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Authors and Affiliations

  1. Southern Federal University, Rostov-on-Don, Russia

    A. V. Abanin

  2. Southern Mathematical Institute, Vladikavkaz, Russia

    A. V. Abanin & V. A. Varziev

Authors
  1. A. V. Abanin
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  2. V. A. Varziev
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Correspondence to A. V. Abanin.

Additional information

Original Russian Text Copyright © 2013 Abanin A.V. and Varziev V.A.

The authors were supported by the Ministry for Education and Science of the Russian Federation (Contracts 14.A18.21.0356 and 8210) and Southern Federal University.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 4, pp. 725–741, July–August, 2013.

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Abanin, A.V., Varziev, V.A. Sufficient sets in weighted Fréchet spaces of entire functions. Sib Math J 54, 575–587 (2013). https://doi.org/10.1134/S0037446613040010

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