O. V. Sherstyukova, “The problem on the minimal type of entire functions of order <nobr>$\rho\in(0,1)$</nobr> with positive zeroes of prescribed densities and step”, Ufimsk. Mat. Zh., 2015, Volume 7, Issue 4,Pages <nobr>146

This article is cited in 4 papers

The problem on the minimal type of entire functions of order $\rho\in(0,1)$ with positive zeroes of prescribed densities and step

O. V. Sherstyukova

Moscow State Pedagogical University, Moscow, Russia

Abstract: We consider the problem on the least possible type of entire functions of order $\rho\in(0,1)$, 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.

UDC: 517.547.22

MSC: 30D15

Received: 01.10.2015