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Zapiski Nauchnykh Seminarov POMI, 2014, Volume 424, Pages 141–153 (Mi znsl6011)  
This article is cited in 1 scientific paper (total in 1 paper)

Entire functions with preassigned zero proximate order

A. F. Grishin, Nguyen Van Quynh

V. N. Karazin Kharkiv National University, Kharkiv, Ukraine
Full-text PDF (192 kB) Citations (1)
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Abstract: It is known that if the proximate order $\rho(r)$ is such that $\lim\rho(r)=\rho>0$ ($r\to\infty$), then there exists an entire function $f(z)$ of proximate order $\rho(r)$. In the case where $\rho=0$ the question about the existence of such an entire function has remained open until now. This question is investigated in the paper.
Key words and phrases: entire transcendental function, zero proximate order, $\rho$-trigonometrically convex function.
Received: 14.04.2014
English version:
Journal of Mathematical Sciences (New York), 2015, Volume 209, Issue 5, Pages 753–760
DOI: https://doi.org/10.1007/s10958-015-2523-1
Bibliographic databases:
Document Type: Article
UDC: 517.547.22
Language: Russian
Citation: A. F. Grishin, Nguyen Van Quynh, “Entire functions with preassigned zero proximate order”, Investigations on linear operators and function theory. Part 42, Zap. Nauchn. Sem. POMI, 424, POMI, St. Petersburg, 2014, 141–153; J. Math. Sci. (N. Y.), 209:5 (2015), 753–760
Citation in format AMSBIB
\Bibitem{GriNgu14}
\by A.~F.~Grishin, Nguyen~Van~Quynh
\paper Entire functions with preassigned zero proximate order
\inbook Investigations on linear operators and function theory. Part~42
\serial Zap. Nauchn. Sem. POMI
\yr 2014
\vol 424
\pages 141--153
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6011}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3481446}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2015
\vol 209
\issue 5
\pages 753--760
\crossref{https://doi.org/10.1007/s10958-015-2523-1}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84939473805}
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  • https://www.mathnet.ru/eng/znsl/v424/p141
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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