Subsequences of zeros for classes of entire functions of exponential type distinguished by growth restrictions
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T. Yu. Baĭguskarov, G. R. Talipova and B. N. Khabibullin
Translated by: S. Kislyakov - St. Petersburg Math. J. 28 (2017), 127-151
- DOI: https://doi.org/10.1090/spmj/1442
- Published electronically: February 15, 2017
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Abstract:
Let $M$ be a function subharmonic on the complex plane $\mathbb {C}$, harmonic outside of the real axis, and such that \[ \limsup _{z\to \infty }\frac {M(z)}{|z|}<+\infty ,\quad \int _{-\infty }^{+\infty } \frac {\max \{0, M(x)\}}{x^2} d x<+\infty , \quad M(0)=0, \] 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 $|f(z)|\leq \exp M(z)$ for all $z\in \mathbb {C}$.References
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Bibliographic 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
- 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)
- © Copyright 2017 American Mathematical Society
- Journal: St. Petersburg Math. J. 28 (2017), 127-151
- MSC (2010): Primary 30C15
- DOI: https://doi.org/10.1090/spmj/1442
- MathSciNet review: 3593001