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Mat. Zametki, 2004, Volume 75, Issue 2, Pages 192–207 (Mi mz23)  

This article is cited in 1 scientific paper (total in 1 paper)

A Theorem on the Zeros of Entire Functions and Its Application

V. P. Zastavnyi

Donetsk National University

Abstract: We consider entire functions of exponential type $\le \sigma$ that are bounded and real on $\mathbb R$ and satisfy the estimate $(-1)^k f({k\pi}/{\sigma} +\tau)\ge0$, $k\in \mathbb{Z}$. It is proved that the zeros of such functions are real and simple with the possible exception of points of the form ${k\pi}/{\sigma}+\tau$, which can be zeros of multiplicity at most 2. These results are applied to specific classes of functions and to the problem of the stability of entire functions. We also refine and supplement a few results due to Pólya.

DOI: https://doi.org/10.4213/mzm23

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English version:
Mathematical Notes, 2004, 75:2, 175–189

Bibliographic databases:

UDC: 517.5
Received: 03.08.2000

Citation: V. P. Zastavnyi, “A Theorem on the Zeros of Entire Functions and Its Application”, Mat. Zametki, 75:2 (2004), 192–207; Math. Notes, 75:2 (2004), 175–189

Citation in format AMSBIB
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\by V.~P.~Zastavnyi
\paper A Theorem on the Zeros of Entire Functions and Its Application
\jour Mat. Zametki
\yr 2004
\vol 75
\issue 2
\pages 192--207
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\crossref{https://doi.org/10.4213/mzm23}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2054552}
\zmath{https://zbmath.org/?q=an:1114.30026}
\transl
\jour Math. Notes
\yr 2004
\vol 75
\issue 2
\pages 175--189
\crossref{https://doi.org/10.1023/B:MATN.0000015034.59144.82}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000220006100019}


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  • https://doi.org/10.4213/mzm23
  • http://mi.mathnet.ru/eng/mz/v75/i2/p192

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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. V. P. Zastavnyi, “On Zeros of Entire Functions of Special Form”, Math. Notes, 83:1 (2008), 23–30  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
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