Abstract:
We consider the problem on the least possible type of entire functions of order ρ∈(0,1), whose zeroes lie on a ray and have prescribed densities and step. We prove the exactness of the estimate obtained previously by the author for the type of these functions. We provide a detailed justification for the construction of the extremal entire function in this problem.
Keywords:
type of an entire function, upper, lower densities and step of sequence of zeroes, extremal problem.
Citation:
O. V. Sherstyukova, “The problem on the minimal type of entire functions of order ρ∈(0,1) with positive zeroes of prescribed densities and step”, Ufa Math. J., 7:4 (2015), 140–148
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\by O.~V.~Sherstyukova
\paper The problem on the minimal type of entire functions of order $\rho\in(0,1)$ with positive zeroes of prescribed densities and step
\jour Ufa Math. J.
\yr 2015
\vol 7
\issue 4
\pages 140--148
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\crossref{https://doi.org/10.13108/2015-7-4-140}
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Linking options:
https://www.mathnet.ru/eng/ufa309
https://doi.org/10.13108/2015-7-4-140
https://www.mathnet.ru/eng/ufa/v7/i4/p146
This publication is cited in the following 4 articles:
G. G. Braichev, O. V. Sherstyukova, “On least type of entire function with given subsequence of zeros”, Ufa Math. J., 14:3 (2022), 17–21
G. G. Braichev, “On the Lower Indicator of an Entire Function
with Roots of Zero Lower Density Lying on a Ray”, Math. Notes, 107:6 (2020), 907–919
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
G. G. Braichev, V. B. Sherstyukov, “Sharp bounds for asymptotic characteristics of growth of entire functions with zeros on given sets”, J. Math. Sci., 250:3 (2020), 419–453
Citation in format AMSBIB
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