@article{Baksa_Bandura_Salo_2022, title={Boundedness of the L-index in a direction of the sum and product of slice holomorphic functions in the unit ball}, volume={57}, url={http://www.matstud.org.ua/ojs/index.php/matstud/article/view/336}, DOI={10.30970/ms.57.2.216-224}, abstractNote={<p>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. <br>we study functions which are analytic in intersection of every slice $\{z^0+t\mathbf{b}: t\in\mathbb{C}\}$ with the unit ball <br>$\mathbb{B}^n=\{z\in\mathbb{C}^{n}: \ |z|:=\sqrt{|z|_1^2+\ldots+|z_n|^2}&lt;1\}$ for any <br>$z^0\in\mathbb{B}^n$. For this class of functions <br>there is considered the concept of boundedness of $L$-index in the direction $\mathbf{b},$ where <br>${L}: \mathbb{B}^n\to\mathbb{R}_+$ is a positive continuous function such that <br>$L(z)&gt;\frac{\beta|\mathbf{b}|}{1-|z|}$ and $\beta&gt;1$ is some constant.<br>There are presented sufficient conditions that the sum of slice holomorphic functions of bounded $L$-index in direction <br>belong this class. This class of slice holomorphic functions is closed under the operation of multiplication.</p&gt;}, number={2}, journal={Matematychni Studii}, author={Baksa, V.P. and Bandura, A. I. and Salo, T.M.}, year={2022}, month={Jun.}, pages={216-224} }