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Ufimsk. Mat. Zh., 2012, Volume 4, Issue 1, Pages 29–37 (Mi ufa129)  

This article is cited in 3 scientific papers (total in 3 papers)

Exact estimates of types of entire functions of an order $\rho\in(0;1)$ with zeroes on the ray

G. G. Braichev

Moscow State Pedagogical University, Moscow, Russia

Abstract: This paper is a detailed account of the author's report made during VI Ufa international conference “Complex analysis and differential equations”, devoted to the 70-th anniversary of Corresponding member of RAS V. V. Napalkov. Sharp lower estimates of an entire function type of a finite order with respect to such wellknown characteristics of the distribution of its zeros as the density (conventional and average), step and lacunarity index. The solution of one new extremal problem is also given.

Keywords: type of an entire function, the upper and lower (average) density of zeros, step and lacunarity index of a sequence of zeros.

Full text: PDF file (422 kB)
References: PDF file   HTML file
UDC: 517.547.22
Received: 20.12.2011

Citation: G. G. Braichev, “Exact estimates of types of entire functions of an order $\rho\in(0;1)$ with zeroes on the ray”, Ufimsk. Mat. Zh., 4:1 (2012), 29–37

Citation in format AMSBIB
\Bibitem{Bra12}
\by G.~G.~Braichev
\paper Exact estimates of types of entire functions of an order $\rho\in(0;1)$ with zeroes on the ray
\jour Ufimsk. Mat. Zh.
\yr 2012
\vol 4
\issue 1
\pages 29--37
\mathnet{http://mi.mathnet.ru/ufa129}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. G. G. Braichev, “Exact relationships between certain characteristics of growth for complex sequences”, Ufa Math. J., 5:4 (2013), 16–29  mathnet  crossref  elib
    2. G. G. Braichev, “The exact bounds of lower type magnitude for entire function of order $\rho\in(0,1)$ with zeros of prescribed average densities”, Ufa Math. J., 7:4 (2015), 32–57  mathnet  crossref  isi  elib
    3. V. B. Sherstyukov, “Asimptoticheskie svoistva tselykh funktsii s zadannym zakonom raspredeleniya kornei”, Kompleksnyi analiz. Tselye funktsii i ikh primeneniya, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 161, VINITI RAN, M., 2019, 104–129  mathnet
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