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.
Citation:
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This publication is cited in the following 23 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, “Zadacha Silvestra i mnozhestva edinstvennosti v klassakh tselykh funktsii”, Funktsionalnye prostranstva. Differentsialnye operatory. Problemy
matematicheskogo obrazovaniya, SMFN, 70, no. 1, Rossiiskii universitet druzhby narodov, M., 2024, 25–37
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”, J Math Sci, 2024
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
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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
Citation in format AMSBIB
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