Examining the asymptotic growth behavior of holomorphic and meromorphic functions has significant importance in complex analysis. Estimations of upper bounds for the rate of growth of entire functions are mostly guaranteed. However, the analog estimations for lower bounds of the rate of growth are not always attainable. In this paper, we give the lower rate of growth of the generalized Hadamard product of two entire axially monogenic functions. It has also been shown that the product entire axially monogenic function is of regular growth or perfectly regular growth when its constituent entire axially monogenic functions possess these properties. The investigation of both upper and lower bounds by means of linear transmutation is also provided. Furthermore, some applications related to approximation theory are outlined.

研究全纯和亚纯函数的渐近生长行为在复杂分析中具有重要意义。大部分功能的增长率的上限估计是可以保证的。但是，并非总是能够获得增长率下限的模拟估计。在本文中，我们给出了两个完整的轴向单基因函数的广义Hadamard乘积的较低增长率。还已经表明，当产品的整个轴向单基因功能具有这些特性时，其整个轴向单基因功能具有规则的生长或完全规则的生长。还提供了通过线性变换研究上限和下限的方法。此外，概述了一些与逼近理论有关的应用。