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Perturbations of an Integer Sequence as Zero Sets of Divisors in Some Spaces of Entire Functions

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Abstract

We consider weighted spaces of entire functions obtained as the images of spaces of ultradistributions of minimal type and normal type on the real line under the Fourier–Laplace transform. The divisors of these spaces are studied. Namely, we find conditions on a perturbing sequence under which the sequence of integers perturbed by it will be the zero set of an entire function that is a divisor of one of the above-mentioned spaces.

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Acknowledgments

The author is grateful to the referee for useful remarks and corrections.

Funding

This work was supported by the Russian Science Foundation under grant no. 22-21-00026, https://rscf.ru/en/project/22-21-00026/.

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Authors and Affiliations

  1. Ufa University of Science and Technology, Ufa, 450076, Russia

    N. F. Abuzyarova

  2. Institute of Mathematics with Computing Centre—Subdivision of the Ufa Federal Research Centre of Russian Academy of Sciences, Ufa, 450008, Russia

    N. F. Abuzyarova

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  1. N. F. Abuzyarova
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Correspondence to N. F. Abuzyarova.

Additional information

Translated from Matematicheskie Zametki, 2023, Vol. 113, pp. 633–645 https://doi.org/10.4213/mzm13576.

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Abuzyarova, N.F. Perturbations of an Integer Sequence as Zero Sets of Divisors in Some Spaces of Entire Functions. Math Notes 113, 613–623 (2023). https://doi.org/10.1134/S0001434623050012

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  • DOI: https://doi.org/10.1134/S0001434623050012

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