Uniform estimates for local properties of analytic functions in a complete Reinhardt domain
Анотація
Using recent estimates of maximum modulus for partial derivatives of the analytic functions with bounded $\mathbf{L}$-index in joint variables we describe maximum modulus of these functions at the polydisc skeleton with given radii by the maximum modulus with lesser radii. Such a description is sufficient and necessary condition of boundedness of $\mathbf{L}$-index in joint variables for functions which are analytic in a complete Reinhardt domain. The vector-valued function $\mathbf{L}$ is a positive and continuous function in the domain and its values at a point is greater than reciprocal of distance from the point to the boundary of the Reinhardt domain multiplied by some constant.
Посилання
A. Bandura, T. Salo, O. Skaskiv, Analytic functions in a complete Reinhardt domain having bounded L-index in joint variables, Symmetry, 16 (2024), №3, Article ID: 351. https://doi.org/10.3390/sym16030351
A.I. Bandura, O.B. Skaskiv, Analytic functions in the unit ball of bounded L-index: asymptotic and local properties, Mat. Stud., 48 (2017), №1, №1, 37–73. https://doi.org/10.15330/ms.48.1.37-73
A. Bandura, O. Skaskiv, Asymptotic estimates of entire functions of bounded L-index in joint variables, Novi Sad J. Math., 48 (2018), №1, 103–116. https://doi.org/10.30755/NSJOM.06997
A. Bandura, Composition of entire functions and bounded L-index in direction, Mat. Stud., 47 (2017), №2, 179–184. https://doi.org/10.15330/ms.47.2.179-184
A. Bandura, N. Petrechko, O. Skaskiv, Maximum modulus in a bidisc of analytic functions of bounded L-index and an analogue of Hayman’s theorem, Mat. Bohemica, 143 (2018), №4, 339–354. https://doi.org/10.21136/MB.2017.0110-16
A. Bandura, O. Skaskiv, Slice holomorphic functions in several variables with bounded L-index in direction, Axioms, 8 (2019), №3, Article ID: 88. https://doi.org/10.3390/axioms8030088
A. Bandura, O. Skaskiv, Entire functions of bounded L-index: Its zeros and behavior of partial logarithmic derivatives, J. Complex Analysis, 2017 (2017), 1–10. Article ID: 3253095. https://doi.org/10.1155/2017/3253095
I.M. Hural, About some problem for entire functions of unbounded index in any direction, Mat. Stud., 51 (2019), №1, 107–110. https://doi.org/10.15330/ms.51.1.107-110
V.P. Kostov, A domain free of the zeros of the partial theta function, Mat. Stud., 58 (2022), №2, 142–158. https://doi.org/10.30970/ms.58.2.142-158
A. Kuryliak, O. Skaskiv, Wiman’s type inequality in multiple-circular domain, Axioms, 10 (2021), №4, Article ID: 348. https://doi.org/10.3390/axioms10040348
B. Lepson, Differential equations of infinite order, hyperdirichlet series and entire functions of bounded index, Proc. Sympos. Pure Math., 11 (1968), 298–307.
T.H. Nguyen, On the conditions for a special entire function related to the partial Theta-function and the q-Kummer functions to belong to the Laguerre-Polya class, Comput. Methods Funct. Theory, 22 (2022), №1, 7–25. https://doi.org/10.1007/s40315-021-00361-0
F. Nuray, R.F. Patterson, Vector-valued bivariate entire functions of bounded index satisfying a system of differential equations, Mat. Stud., 49 (2018), №1, 67–74. https://doi.org/10.15330/ms.49.1.67-74
F. Nuray, R.F. Patterson, Entire bivariate functions of exponential type, Bull. Math. Sci., 5 (2015), №2, 171–177. http://dx.doi.org/10.1007/s13373-015-0066-x
F. Nuray, R. F. Patterson, Multivalence of bivariate functions of bounded index, Le Matematiche (Catania), 70 (2015), №2, 225–233. https://doi.org/10.4418/2015.70.2.14
M.M. Sheremeta, A.D. Kuzyk, Logarithmic derivative and zeros of an entire function of bounded l-index, Sib. Math. J., 33 (1992), №2, 304–312. https://doi.org/10.1007/BF00971102
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