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Representing Systems of Exponents in Weight Subspaces H (D)

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Abstract

In this paper, weight subspaces of the space of analytic functions on a bounded convex domain of the complex plane are considered. Descriptions of spaces that are strongly dual to the inductive and projective limits of uniformly weight spaces of analytic functions in a bounded convex domain D ⊂ ℂ are obtained in terms of the Fourier–Laplace transform. For each normed, uniformly weight space H(D, u), we construct the minimal vector space ℋi(D, u) containing H(D, u) and invariant under differentiation and the maximal vector space ℋp(D, u) contained in H(D, u) and invariant under differentiation. We introduce natural locally convex topologies on these spaces and describe strongly dual spaces in terms of the Fourier–Laplace transform. The existence of representing exponential systems in the space ℋi(D, u) is proved.

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Authors and Affiliations

  1. Bashkir State University, Ufa, Russia

    R. A. Bashmakov, K. P. Isaev & R. S. Yulmukhametov

  2. Institute of Mathematics with Computing Center, Ufa Federal Research Center of the Russian Academy of Sciences, Ufa, Russia

    K. P. Isaev & R. S. Yulmukhametov

Authors
  1. R. A. Bashmakov
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  2. K. P. Isaev
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  3. R. S. Yulmukhametov
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Correspondence to R. A. Bashmakov.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 153, Complex Analysis, 2018.

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Bashmakov, R.A., Isaev, K.P. & Yulmukhametov, R.S. Representing Systems of Exponents in Weight Subspaces H (D). J Math Sci 252, 302–318 (2021). https://doi.org/10.1007/s10958-020-05162-9

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  • DOI: https://doi.org/10.1007/s10958-020-05162-9

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