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Mat. Sb., 2009, Volume 200, Number 2, Pages 129–158 (Mi msb3885)  

This article is cited in 12 scientific papers (total in 12 papers)

Zero sequences of holomorphic functions, representation of meromorphic functions. II. Entire functions

B. N. Khabibullinab

a Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
b Bashkir State University, Faculty of Mathematics

Abstract: Let $\Lambda=\{\lambda_k\}$ be a sequence of points in the complex plane $\mathbb C$ and $f$ a non-trivial entire function of finite order $\rho$ and finite type $\sigma$ such that $f=0$ on $\Lambda$. Upper bounds for functions such as the Weierstrass-Hadamard canonical product of order $\rho$ constructed from the sequence $\Lambda$ are obtained. Similar bounds for meromorphic functions are also derived. These results are used to estimate the radius of completeness of a system of exponentials in $\mathbb C$.
Bibliography: 26 titles.

Keywords: function, zero sequence, subharmonic function, radius of completeness, system of exponentials.


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English version:
Sbornik: Mathematics, 2009, 200:2, 283–312

Bibliographic databases:

UDC: 517.547.2+517.538.2+517.581+517.574
MSC: 30C15, 30D15, 30D30
Received: 22.05.2007 and 12.08.2008

Citation: B. N. Khabibullin, “Zero sequences of holomorphic functions, representation of meromorphic functions. II. Entire functions”, Mat. Sb., 200:2 (2009), 129–158; Sb. Math., 200:2 (2009), 283–312

Citation in format AMSBIB
\by B.~N.~Khabibullin
\paper Zero sequences of holomorphic functions, representation of meromorphic functions. II.~Entire functions
\jour Mat. Sb.
\yr 2009
\vol 200
\issue 2
\pages 129--158
\jour Sb. Math.
\yr 2009
\vol 200
\issue 2
\pages 283--312

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    This publication is cited in the following articles:
    1. G. G. Braichev, V. B. Sherstyukov, “On the least possible type of entire functions of order $\rho\in(0,1)$ with positive zeros”, Izv. Math., 75:1 (2011), 1–27  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. G. G. Braichev, V. B. Sherstyukov, “On the Growth of Entire Functions with Discretely Measurable Zeros”, Math. Notes, 91:5 (2012), 630–644  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. G. G. Braichev, “The least type of an entire function of order $\rho\in(0,1)$ having positive zeros with prescribed averaged densities”, Sb. Math., 203:7 (2012), 950–975  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. “Sharp bounds for the type of an entire function of order less than 1 whose zeros are located on a ray and have given averaged densities”, Dokl. Math., 86:1 (2012), 559–561  crossref  mathscinet  zmath  isi  elib  scopus
    5. K. G. Malyutin, I. I. Kozlova, N. Sadik, “Canonical Functions of Admissible Measures in the Half-Plane”, Math. Notes, 96:3 (2014), 391–402  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. F. S. Myshakov, “An Analog of the Valiron–Goldberg Theorem under a Restriction Condition on the Averaged Counting Function of Zeros”, Math. Notes, 96:5 (2014), 831–835  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. G. G. Braichev, “Sharp Estimates of Types of Entire Functions with Zeros on Rays”, Math. Notes, 97:4 (2015), 510–520  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. 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
    9. V. B. Sherstyukov, “Minimal value for the type of an entire function of order $\rho\in(0,1)$, whose zeros lie in an angle and have a prescribed density”, Ufa Math. J., 8:1 (2016), 108–120  mathnet  crossref  isi  elib
    10. G. G. Braichev, V. B. Sherstyukov, “Tochnye otsenki asimptoticheskikh kharakteristik rosta tselykh funktsii s nulyami na zadannykh mnozhestvakh”, Fundament. i prikl. matem., 22:1 (2018), 51–97  mathnet
    11. 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  mathscinet
    12. A. F. Kuzhaev, “On the necessary and sufficient conditions for the measurability of a positive sequence”, Probl. anal. Issues Anal., 8(26):3 (2019), 63–72  mathnet  crossref  elib
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