右半平面上解析的Laplace-Stieltjes变换对数级

ON THE LOGARITHMIC ORDER OF LAPLACE-STIELTJES TRANSFORMATIONS CONVERGENT IN THE RIGHT HALF-PLANE

本文研究了零级Laplace-Stieltjes变换的增长性问题.利用对数级和对数下级的定义,获得了这类变换具有对数级的特征,即变换的对数级和对数下级与其系数之间的关系,推广了Dirichlet级数的相关结果.

In this paper,the growth of the Laplace-Stieltjes transforms of zero order convergent in right half-plane is investigated.By using the definition of logarithmic order and lower logarithmic order,the relations between logarithmic order and lower logarithmic order and ＂coefficients＂ of the transformations is obtained.Some results of Dirichlet series are improved.