Boundedness of the L-index in a direction of the sum and product of slice holomorphic functions in the unit ball

  • V.P. Baksa Lviv Politechnic National University
  • A. I. Bandura Ivano-Frankivsk National Tecnical University of OIl and Gas
  • T.M. Salo Lviv Politechnic National University

Анотація

Let $\mathbf{b}\in\mathbb{C}^n\setminus\{\mathbf{0}\}$ be a fixed direction. We consider slice holomorphic functions of several complex variables in the unit ball, i.e.
we study functions which are analytic in intersection of every slice $\{z^0+t\mathbf{b}: t\in\mathbb{C}\}$ with the unit ball
$\mathbb{B}^n=\{z\in\mathbb{C}^{n}: \ |z|:=\sqrt{|z|_1^2+\ldots+|z_n|^2}<1\}$ for any
$z^0\in\mathbb{B}^n$. For this class of functions
there is considered the concept of boundedness of $L$-index in the direction $\mathbf{b},$ where
${L}: \mathbb{B}^n\to\mathbb{R}_+$ is a positive continuous function such that
$L(z)>\frac{\beta|\mathbf{b}|}{1-|z|}$ and $\beta>1$ is some constant.
There are presented sufficient conditions that the sum of slice holomorphic functions of bounded $L$-index in direction
belong this class. This class of slice holomorphic functions is closed under the operation of multiplication.

Посилання

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Опубліковано
2022-06-27
Як цитувати
Baksa, V., Bandura, A. I., & Salo, T. (2022). Boundedness of the L-index in a direction of the sum and product of slice holomorphic functions in the unit ball. Математичні студії, 57(2), 216-224. https://doi.org/10.30970/ms.57.2.216-224
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