The growth and value distribution of Laplace-Stieltjes transformations with infinite order in the right half-plane
The growth and value distribution of Laplace-Stieltjes transformations with infinite order in the right half-plane
复制标题
右半平面无限阶Laplace-Stiltjes变换的增长和值分布
DOI：
10.1186/1029-242x-2013-273
复制
发表时间：
2013-01-01
影响因子：
1.6
通讯作者：
Xuan, Zu-Xing
中科院分区：
文献类型：
--
作者：
Xu, Hong-Yan;Xuan, Zu-Xing
通过引入XU级函数的概念，研究了由Laplace-Stieltjes变换定义的收敛于右半平面的解析函数的增长性.得到了这类函数的有限XU级的一些充要条件。我们还研究了具有有限XU-阶的Laplace-Stieltjes变换的值分布，得到了XU-点的存在性以及处理两个收敛于右半平面的Laplace-Stieltjes变换的重值的XU-点的存在性.本文的主要结果是对尚和高给出的几个定理的改进和推广。
By introducing the concept of XU-order functions, we study the growth of analytic functions defined by Laplace-Stieltjes transformations which converge on the right half-plane. Some necessary and sufficient conditions on finite XU-order of these functions have been obtained. We also investigate the value distribution of Laplace-Stieltjes transformations with finite XU-order and obtain the existence of XU-points and XU-points dealing with multiple values of two Laplace-Stieltjes transformations which converge on the right half-plane. The main results of this paper are improvement and extension of some theorems given by Shang and Gao.MSC:44A10, 30D15.