This article is cited in 10 papers

On a Class of Sine-Type Functions

A. A. Yukhimenko

M. V. Lomonosov Moscow State University

Abstract: We study an infinite product $F_\Lambda(z)$ with zeros $\lambda_n=n+l(|n|)$, $n\in\mathbb Z$, where $l(t)$ is a concave function and $l(t)=o(t)$. We obtain a test for $F_\Lambda(z)$ to belong to the class of sine-type functions. For the particular case in which $l(t)$ is a regularly varying function, we obtain sharp asymptotic estimates for $F_\Lambda(z)$.

Keywords: sine-type function, concave function, regularly varying function, hypergeometric function, Riesz basis, analytic function.

UDC: 517.547.2+517.538.2

Received: 03.07.2007
Revised: 11.11.2007

DOI: 10.4213/mzm4056

 English version: Mathematical Notes, 2008, 83:6, 858–870

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