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Matematicheskie Zametki, 2008, Volume 83, Issue 6, Pages 941–954
DOI: https://doi.org/10.4213/mzm4056 (Mi mzm4056) 		 
This article is cited in 8 scientific papers (total in 8 papers)

On a Class of Sine-Type Functions

A. A. Yukhimenko

M. V. Lomonosov Moscow State University
Full-text PDF (500 kB) Citations (8)
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DOI: https://doi.org/10.4213/mzm4056
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.
Received: 03.07.2007
Revised: 11.11.2007
English version:
Mathematical Notes, 2008, Volume 83, Issue 6, Pages 858–870
DOI: https://doi.org/10.1134/S0001434608050313
Bibliographic databases:
UDC: 517.547.2+517.538.2
Language: Russian
Citation: A. A. Yukhimenko, “On a Class of Sine-Type Functions”, Mat. Zametki, 83:6 (2008), 941–954; Math. Notes, 83:6 (2008), 858–870
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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