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Russian Mathematics

, Volume 63, Issue 1, pp 24–34 | Cite as

Representing Systems of Exponentials in Projective Limits of Weighted Subspaces of A(D)

  • K. P. IsaevEmail author
Article
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Abstract

We introduce a normed space of functions, holomorphic in a bounded convex domain. Its elements are infinitely differentiable up to the boundary, and all their derivatives satisfy estimates specified by a convex sequence of positive numbers. We consider its largest linear subspace that is invariant with respect to the operator of differentiation and provide it with the natural topology of projective limit. We establish duality between this subspace and some space of entire functions. Based on this, we construct a representing system of exponentials in the subspace.

Key words

analytic function weighted space locally convex space sufficient set representing system of exponentials 

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Notes

Acknowledgments

Supported by the Russian Foundation for Basic Research, project No. 18-01-00095 A.

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© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.Institute of Mathematics with Computer Center of the Ufa Science Center of the Russian Academy of SciencesUfaRussia
  2. 2.Bashkirian State UniversityUfaRussia

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