Some criteria of boundedness of the L-index in direction for slice holomorphic functions of several complex variables

被引：0

作者：

Bandura A. ^{[1
]}

Skaskiv O. ^{[2
]}

机构：

[1] Ivano-Frankivs’k National Technical University of Oil and Gas, Ivano-Frankivs’k

[2] Ivan Franko National University of Lviv, Lviv

来源：

Journal of Mathematical Sciences | 2020年 / 244卷 / 1期

关键词：

Bounded index; bounded l-index; bounded L-index in direction; directional derivative; distribution of zeros; existence theorem; holomorphic function; logarithmic derivative; maximum modulus; minimum modulus; slice function;

D O I：

10.1007/s10958-019-04600-7

中图分类号：

学科分类号：

摘要：

We investigate the slice holomorphic functions of several complex variables that have a bounded L-index in some direction and are entire on every slice {z0 + tb : t ∈ ℂ} for every z0 ∈ ℂn and for a given direction b ∈ ℂn {0}. For this class of functions, we prove some criteria of boundedness of the L-index in direction describing a local behavior of the maximum and minimum moduli of a slice holomorphic function and give estimates of the logarithmic derivative and the distribution of zeros. Moreover, we obtain analogs of the known Hayman theorem and logarithmic criteria. They are applicable to the analytic theory of differential equations. We also study the value distribution and prove the existence theorem for those functions. It is shown that the bounded multiplicity of zeros for a slice holomorphic function F : ℂn → ℂ is the necessary and sufficient condition for the existence of a positive continuous function L : ℂn → ℝ+ such that F has a bounded L-index in direction. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

引用

页码：1 / 21

页数：20

共 31 条

[1]

Bandura A.I., Skaskiv O.B., Slice holomorphic functions in several variables having bounded L-index in direction, Axioms, 8, 3, (2019)

[2]

Bandura A.I., Analytic functions in the unit ball of bounded value L-distribution in direction, Mat. Stud., 49, 1, pp. 75-79, (2018)

[3]

Bandura A.I., Product of two entire functions of bounded L-index in direction is a function with the same class, Bukovyn. Mat. Zh., 4, 1-2, pp. 8-12, (2016)

[4]

Bandura A.I., Skaskiv O.B., Sufficient conditions of boundedness of L-index and analog of Hayman’s theorem for analytic functions in a ball, Stud. Univ. Babe, s-Bolyai Math., 63, 4, pp. 483-501, (2018)

[5]

Bandura A.I., Skaskiv O.B., Analytic functions in the unit ball of bounded L-index in joint variables and of bounded L-index in direction: a connection between these classes, Demonstr. Math., 52, 1, pp. 82-87, (2019)

[6]

Bandura A.I., Skaskiv O.B., Entire functions of bounded L-index in direction, Mat. Stud., 27, 1, pp. 30-52, (2007)

[7]

Bandura A.I., Skaskiv O.B., Boundedness of L-index in direction of functions of the form f(⟨z,m⟩) and existence theorems, Mat. Stud., 41, 1, pp. 45-52, (2014)

[8]

Bandura A., Skaskiv O., Entire Functions of Several Variables of Bounded Index, (2016)

[9]

Bandura A., Petrechko N., Skaskiv O., Maximum modulus in a bidisc of analytic functions of bounded L-index and an analogue of Hayman’s theorem, Mat. Bohemica, 143, 4, pp. 339-354, (2018)

[10]

Bandura A., Skaskiv O., Directional logarithmic derivative and the distribution of zeros of an entire function of bounded L-index along the direction, Ukr. Math. J., 69, 3, pp. 500-508, (2017)

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