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This article is cited in 23 scientific papers (total in 23 papers)
On the least possible type of entire functions of order $\rho\in(0,1)$ with positive zeros
G. G. Braichev, V. B. Sherstyukov National Engineering Physics Institute "MEPhI"
Abstract:
We find the greatest lower bound for the type of an entire function of order
$\rho\in(0,1)$ whose sequence of zeros lies on one ray and has prescribed
lower and upper $\rho$-densities. We make a thorough study of the dependence
of this extremal quantity on $\rho$ and on properties of the distribution
of zeros. The results are applied to an extremal problem on the radii
of completeness of systems of exponentials.
Keywords:
extremal problems, type of entire function, upper and lower densities of zeros,
completeness of systems of exponentials.
Received: 06.04.2009 Revised: 31.08.2009
Citation:
G. G. Braichev, V. B. Sherstyukov, “On the least possible type of entire functions of order $\rho\in(0,1)$ with positive zeros”, Izv. Math., 75:1 (2011), 1–27
Linking options:
https://www.mathnet.ru/eng/im4104https://doi.org/10.1070/IM2011v075n01ABEH002525 https://www.mathnet.ru/eng/im/v75/i1/p3
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Abstract page: | 1374 | Russian version PDF: | 239 | English version PDF: | 17 | References: | 76 | First page: | 35 |
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