B. N. Khabibullin, “Zero sequences of holomorphic functions, representation of meromorphic functions. II. Entire functions”, Sb. Math., 200:2 (2009), 283

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Sbornik: Mathematics, 2009, Volume 200, Issue 2, Pages 283–312
DOI: https://doi.org/10.1070/SM2009v200n02ABEH003996 (Mi sm3885)

This article is cited in 22 scientific papers (total in 22 papers)

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

B. N. Khabibullin^ab

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

English version PDF (526 kB) Citations (22) Russian version article

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DOI: https://doi.org/10.1070/SM2009v200n02ABEH003996

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.

Received: 22.05.2007 and 12.08.2008

Bibliographic databases:

UDC: 517.547.2+517.538.2+517.581+517.574

MSC: 30C15, 30D15, 30D30

Language: English

Original paper language: Russian

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

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/sm3885

https://doi.org/10.1070/SM2009v200n02ABEH003996

https://www.mathnet.ru/eng/sm/v200/i2/p129

Cycle of papers

Zero sequences of holomorphic functions, representation of meromorphic functions, and harmonic minorants
B. N. Khabibullin
Mat. Sb., 2007, 198:2, 121–160
Zero sequences of holomorphic functions, representation of meromorphic functions. II. Entire functions
B. N. Khabibullin
Mat. Sb., 2009, 200:2, 129–158

This publication is cited in the following 22 articles:

B. N. Khabibullin, “Distributions of zeros and masses of entire and subharmonic functions with restrictions on their growth along the strip”, Izv. Math., 88:1 (2024), 133–193
G. G. Braichev, V. B. Sherstyukov, “Uniqueness Theorem for Entire Functions of Exponential Type”, Lobachevskii J Math, 45:6 (2024), 2672
G. G. Braichev, “The Sylvester problem and uniqueness sets in classes of entire functions”, Journal of Mathematical Sciences, 286:1 (2024), 22–34
G. G. Braichev, “On the Connection between the Growth of Zeros and the Decrease of Taylor Coefficients of Entire Functions”, Math. Notes, 113:1 (2023), 27–38
B. N. Khabibullin, E. G. Kudasheva, A. E. Salimova, “Kriterii polnoty eksponentsialnoi sistemy v geometricheskikh terminakh shiriny v napravlenii”, Differentsialnye uravneniya i matematicheskaya fizika, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 225, VINITI RAN, M., 2023, 150–159
A. M. Gaisin, B. E. Kanguzhin, A. A. Seitova, “Completeness of the exponential system on a segment of the real axis”, Eurasian Math. J., 13:2 (2022), 37–42
G. G. Braichev, O. V. Sherstyukova, “On least type of entire function with given subsequence of zeros”, Ufa Math. J., 14:3 (2022), 17–21
B. N. Khabibullin, E. B. Menshikova, “Preorders on Subharmonic Functions and Measures with Applications to the Distribution of Zeros of Holomorphic Functions”, Lobachevskii J Math, 43:3 (2022), 587
Khabibullin B.N. Menshikova E.B., “Balayage of Measures With Respect to Polynomials and Logarithmic Kernels on the Complex Plane”, Lobachevskii J. Math., 42:12 (2021), 2823–2833
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
V. B. Sherstyukov, “Asymptotic properties of entire functions with given laws of distribution of zeros”, J. Math. Sci. (N. Y.), 257:2 (2021), 246–272
G. G. Braichev, V. B. Sherstyukov, “Sharp bounds for asymptotic characteristics of growth of entire functions with zeros on given sets”, J. Math. Sci., 250:3 (2020), 419–453
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
G. G. Braichev, “Sharp Estimates of Types of Entire Functions with Zeros on Rays”, Math. Notes, 97:4 (2015), 510–520
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
F. S. Myshakov, “Analog teoremy Valirona—Goldberga pri ogranichenii na usrednennuyu schitayuschuyu funktsiyu mnozhestva kornei”, Anal Math, 41:3 (2015), 175
K. G. Malyutin, I. I. Kozlova, N. Sadik, “Canonical Functions of Admissible Measures in the Half-Plane”, Math. Notes, 96:3 (2014), 391–402
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
G. G. Braichev, V. B. Sherstyukov, “On the Growth of Entire Functions with Discretely Measurable Zeros”, Math. Notes, 91:5 (2012), 630–644
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	156
First page:	25

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