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Generating Functions for Bases in Hilbert Spaces of Entire Functions

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Abstract

We prove that unconditional bases in a functional Hilbert space H have a generating function if and only if the space H is stable. Necessary and sufficient conditions for the stability of spaces adjoint to weighted spaces on an interval are obtained.

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Authors and Affiliations

  1. Institute of Mathematics with Computer Center of the Russian Academy of Sciences, Ufa, Russia

    K. P. Isaev & R. S. Yulmukhametov

  2. Bashkir State University, Ufa, Russia

    K. P. Isaev, A. V. Lutsenko & R. S. Yulmukhametov

Authors
  1. K. P. Isaev
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  2. A. V. Lutsenko
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  3. R. S. Yulmukhametov
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Corresponding author

Correspondence to K. P. Isaev.

Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 142, Complex Analysis, 2017.

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Isaev, K.P., Lutsenko, A.V. & Yulmukhametov, R.S. Generating Functions for Bases in Hilbert Spaces of Entire Functions. J Math Sci 241, 718–726 (2019). https://doi.org/10.1007/s10958-019-04457-w

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  • DOI: https://doi.org/10.1007/s10958-019-04457-w

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