Some Results on Composition of Analytic Functions in a Unit Polydisc

Andriy Bandura; Petro Kurliak; Oleh Skaskiv

doi:10.32323/ujma.1444221

EN

Some Results on Composition of Analytic Functions in a Unit Polydisc

Abstract

The manuscript is an attempt to consider all methods which are applicable to investigation a directional index for composition of an analytic function in some domain and an entire function. The approaches are applied to find sufficient conditions of the $L$-index boundedness in a direction $\mathbf{b}\in\mathbb{C}^n\setminus\{\mathbf{0}\}$, where the continuous function $L$ satisfies some growth condition and the condition of positivity in the unit polydisc. The investigation is based on a counterpart of the Hayman Theorem for the class of analytic functions in the polydisc and a counterpart of logarithmic criterion describing local conduct of logarithmic derivative modulus outside some neighborhoods of zeros. The established results are new advances for the functions analytic in the polydisc and in multidimensional value distribution theory.

Keywords

Analytic function, Finite directional $L$-index, Boundedness of $L$-index in a direction, $L$-index in direction, Composition, Directional derivative, Entire function, Several complex variables, Unit polydisc

References

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Details

Primary Language

English

Subjects

Pure Mathematics (Other)

Journal Section

Research Article

Authors

Andriy Bandura ^*
0000-0003-0598-2237
Ukraine

Petro Kurliak
0000-0001-8113-5211
Ukraine

Oleh Skaskiv
0000-0001-5217-8394
Ukraine

Early Pub Date

August 25, 2024

Publication Date

September 21, 2024

Submission Date

February 28, 2024

Acceptance Date

July 31, 2024

Published in Issue

Year 2024 Volume: 7 Number: 3

DOI

https://doi.org/10.32323/ujma.1444221

IZ

https://izlik.org/JA74BD48NY

APA

Bandura, A., Kurliak, P., & Skaskiv, O. (2024). Some Results on Composition of Analytic Functions in a Unit Polydisc. Universal Journal of Mathematics and Applications, 7(3), 121-128. https://doi.org/10.32323/ujma.1444221

AMA

1.Bandura A, Kurliak P, Skaskiv O. Some Results on Composition of Analytic Functions in a Unit Polydisc. Univ. J. Math. Appl. 2024;7(3):121-128. doi:10.32323/ujma.1444221

Chicago

Bandura, Andriy, Petro Kurliak, and Oleh Skaskiv. 2024. “Some Results on Composition of Analytic Functions in a Unit Polydisc”. Universal Journal of Mathematics and Applications 7 (3): 121-28. https://doi.org/10.32323/ujma.1444221.

EndNote

Bandura A, Kurliak P, Skaskiv O (September 1, 2024) Some Results on Composition of Analytic Functions in a Unit Polydisc. Universal Journal of Mathematics and Applications 7 3 121–128.

IEEE

[1]A. Bandura, P. Kurliak, and O. Skaskiv, “Some Results on Composition of Analytic Functions in a Unit Polydisc”, Univ. J. Math. Appl., vol. 7, no. 3, pp. 121–128, Sept. 2024, doi: 10.32323/ujma.1444221.

ISNAD

Bandura, Andriy - Kurliak, Petro - Skaskiv, Oleh. “Some Results on Composition of Analytic Functions in a Unit Polydisc”. Universal Journal of Mathematics and Applications 7/3 (September 1, 2024): 121-128. https://doi.org/10.32323/ujma.1444221.

JAMA

1.Bandura A, Kurliak P, Skaskiv O. Some Results on Composition of Analytic Functions in a Unit Polydisc. Univ. J. Math. Appl. 2024;7:121–128.

MLA

Bandura, Andriy, et al. “Some Results on Composition of Analytic Functions in a Unit Polydisc”. Universal Journal of Mathematics and Applications, vol. 7, no. 3, Sept. 2024, pp. 121-8, doi:10.32323/ujma.1444221.

Vancouver

1.Andriy Bandura, Petro Kurliak, Oleh Skaskiv. Some Results on Composition of Analytic Functions in a Unit Polydisc. Univ. J. Math. Appl. 2024 Sep. 1;7(3):121-8. doi:10.32323/ujma.1444221