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Sbornik: Mathematics, 2018, Volume 209, Issue 6, Pages 871–900
DOI: https://doi.org/10.1070/SM8885 (Mi sm8885) 		 
Asymptotic behaviour of even canonical products with slight abnormalities in the distribution of the set of zeros, which has positive density

V. N. Seliverstov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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DOI: https://doi.org/10.1070/SM8885
Abstract: The asymptotic behaviour of even canonical products with zeros on the real axis is considered. It is assumed that the set of zeros has density (the sequence $\pm \lambda_{n}$ has density). Sharp asymptotic estimates for the logarithm of the modulus of the canonical product are obtained under certain restrictions on the rate of convergence of the ratio $n/\lambda_{n}$ to its limit.
Bibliography: 8 titles.
Keywords: even canonical product, regularly varying function, asymptotic estimate.
Received: 15.12.2016 and 29.06.2017
Russian version:
Matematicheskii Sbornik, 2018, Volume 209, Number 6, Pages 98–127
DOI: https://doi.org/10.4213/sm8885
Bibliographic databases:
Document Type: Article
UDC: 517.547.22
MSC: 30D15
Language: English
Original paper language: Russian
Citation: V. N. Seliverstov, “Asymptotic behaviour of even canonical products with slight abnormalities in the distribution of the set of zeros, which has positive density”, Mat. Sb., 209:6 (2018), 98–127; Sb. Math., 209:6 (2018), 871–900
Citation in format AMSBIB
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    References:34
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