The indicator of entire functions with rapidly oscillating coefficients

Author P. V. Filevych

S.Z. Gzhytskyy Lviv National University of Veterinary Medicine and Biotechnologies

Abstract Let $f(z)=\sum_{n=0}^\infty c_nz^n$ be an entire function of order $\rho_f\in(0,+\infty)$, let $\sigma_f$ and $h_f(\theta)$ be the type and the indicator of the function $f$, respectively, let $(p_n)$ be a sequence of positive integers with Hadamard gaps and $f_t(z)=\sum_{n=0}^\infty e^{ip_nt}c_nz^n$, where $t\in\mathbb{R}$. Then, for almost every $t\in\mathbb{R}$, the equality $h_{f_t}(\theta)=\sigma_f$ holds for every $\theta\in\mathbb{R}$.
Keywords indicator of entire function; Hadamard gap
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Pages 142-148
Volume 35
Issue 2
Year 2011
Journal Matematychni Studii
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