Asymptotic behavior of averaging of entire functions of improved regular growth

Abstract

Using the Fourier series method for entire functions, we investigate the asymptotic behavior of averaging of entire functions of improved regular growth.

Asymptotic behavior of entire functions of improved regular growth in the metric of $L^p[0, 2\pi]$

“…The aim of the present paper is obtain an analog of Theorem A for entire functions of improved regular growth with zeros on a finite system of rays (see [4,7,8,9,10,14]). …”

“…An entire function f is called a function of improved regular growth (see [7,8,9,10,14]) if for some ρ ∈ (0, +∞) and ρ 1 ∈ (0, ρ), and a 2π-periodic ρ-trigonometrically convex function h(ϕ) ≡ −∞ there exists the set U ⊂ C contained in the union of disks with finite sum of radii and such that log…”

Regular growth of Fourier coefficients of the logarithmic derivative of entire functions of improved regular growth

“…In [7,15] (see also [8,9,10,14]), the notion of entire function of improved regular growth was introduced, and a criterion for this regularity was obtained in terms of the distribution of zeros under the condition that they are located on a nite system of rays. In [6], this notion was generalized to subharmonic functions.…”

“…Criterion for the improved regular growth of entire functions of positive order with zeros on a nite system of rays in terms of their Fourier coecients was established in [8]. Asymptotic behavior of entire functions of improved regular growth with zeros on a nite system of rays in the metric of L p [0, 2π] was described in [10].…”