Abstract:
Canonical products with symmetrically positioned real zeros are considered. The question of the measurability of the sequence of zeros in terms of the weighted condensation index is treated. A natural class of weight functions, for which a finite condensation index ensures that the sequence of zeros is measurable, is distinguished. The main
condition characterizing this class is shown to be sharp.
Bibliography: 31 titles.
Keywords:
canonical product, measurable sequence of zeros, condensation index.
\Bibitem{She15}
\by V.~B.~Sherstyukov
\paper Distribution of the zeros of canonical products and weighted condensation index
\jour Sb. Math.
\yr 2015
\vol 206
\issue 9
\pages 1299--1339
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Linking options:
https://www.mathnet.ru/eng/sm8446
https://doi.org/10.1070/SM2015v206n09ABEH004497
https://www.mathnet.ru/eng/sm/v206/i9/p139
This publication is cited in the following 5 articles:
E. D. Alferova, V. B. Sherstyukov, “Calculation of the Limit of a Special Sequence of Trigonometric Functions”, Math. Notes, 115:2 (2024), 269–274
K. G. Malyutin, T. I. Malyutina, T. V. Shevtsova, “Azarin limiting sets of functions and asymptotic representation of integrals”, Ufa Math. J., 11:2 (2019), 97–113
V. B. Sherstyukov, “Asymptotic properties of entire functions with given laws of distribution of zeros”, J. Math. Sci. (N. Y.), 257:2 (2021), 246–272
V. N. Seliverstov, “Asymptotic behaviour of even canonical products with slight abnormalities in the distribution of the set of zeros, which has positive density”, Sb. Math., 209:6 (2018), 871–900
K. G. Malyutin, “Interpolation Problems of A. F. Leontiev Type”, J. Math. Sci. (N. Y.), 252:3 (2021), 399–419
Citation in format AMSBIB
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