This article is cited in 22 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.

UDC: 517.547.22

MSC: 30D20, 30C15, 30D15, 46B15

Received: 06.04.2009
Revised: 31.08.2009

DOI: 10.4213/im4104

 English version: Izvestiya: Mathematics, 2011, 75:1, 1–27

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