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Subsequences of zeros for classes of entire functions of exponential type distinguished by growth restrictions


Authors: T. Yu. Baĭguskarov, G. R. Talipova and B. N. Khabibullin
Translated by: S. Kislyakov
Original publication: Algebra i Analiz, tom 28 (2016), nomer 2.
Journal: St. Petersburg Math. J. 28 (2017), 127-151
MSC (2010): Primary 30C15
DOI: https://doi.org/10.1090/spmj/1442
Published electronically: February 15, 2017
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ M$ be a function subharmonic on the complex plane $ \mathbb{C}$, harmonic outside of the real axis, and such that

$\displaystyle \limsup _{z\to \infty }\frac {M(z)}{\vert z\vert}<+\infty ,\quad ... ...ty }^{+\infty } \frac {\max \{0, M(x)\}}{x^2} \, d x<+\infty , \enskip M(0)=0, $

and $ M(z)=M(\overline z)$ for all $ z\in \mathbb{C}$. A description is given for all sequences of points in $ \mathbb{C}$ that are included in the zero set of some nonzero entire function $ f$ with $ \vert f(z)\vert\leq \exp M(z)$ for all $ z\in \mathbb{C}$.

References [Enhancements On Off] (What's this?)

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Additional Information

T. Yu. Baĭguskarov
Affiliation: Department of Mathematics and Informatics, Bashkir State University, ul. Zaki Validi 32, 450074 Ufa, Bashkortostan, Russia
Email: t.bayguskarov@gmail.com

G. R. Talipova
Affiliation: Department of Mathematics and Informatics, Bashkir State University, ul. Zaki Validi 32, 450074 Ufa, Bashkortostan, Russia

B. N. Khabibullin
Affiliation: Department of Mathematics and Informatics, Bashkir State University, ul. Zaki Validi 32, 450074 Ufa, Bashkortostan, Russia
Email: Khabib-Bulat@mail.ru

DOI: https://doi.org/10.1090/spmj/1442
Keywords: Entire function, sequence of zeros, subharmonicity, Cartwright class, balayage, Jensen measure
Received by editor(s): March 22, 2015
Published electronically: February 15, 2017
Additional Notes: The authors were supported by RFBR (grant no. 16–01–00024a)
Article copyright: © Copyright 2017 American Mathematical Society

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