广义Laplace-Stieltjes变换的增长性

The growth of generalized Laplace-Stieltjes transforms

研究由广义Laplace-Stieltjes变换所表示整函数的er级和精确级,给出广义Laplace-Stieltjes变换所表示的整函数的最大模和en的定义;引进er级,得到er级和An,ωn之间的关系;引进精确级,得到由广义Laplace-Stieltjes变换所表示的整函数的精确级和An,ωn之间的关系。最后得到广义Laplace-Stieltjes变换的特殊情况即为Laplace-Stieltjes变换时的相关结果。

The e^r order and precision order of entire functions represented by generalized Laplace-Stiehjes transforms are mainly studied. The definitions of the maximal modular and An of entire functions represented by generalized Laplace-Stiehjes transforms are given firstly. Nexfly, the e^r order is introduced and the relation between e^r order and An ,ωn is obtained. Finally, results of the Laplace-Stieltjes transform which is a special case of the generalized Laplace-Stieltjes transform are given.