TY - JOUR AU - Baksa, V.P. AU - Bandura, A. I. AU - Salo, T.M. PY - 2022/06/27 Y2 - 2024/03/29 TI - Boundedness of the L-index in a direction of the sum and product of slice holomorphic functions in the unit ball JF - Matematychni Studii JA - Mat. Stud. VL - 57 IS - 2 SE - Articles DO - 10.30970/ms.57.2.216-224 UR - http://www.matstud.org.ua/ojs/index.php/matstud/article/view/336 SP - 216-224 AB - 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. ER -