On the growth properties of the Laplace–Stieltjes transform

Abstract

In this paper, we investigate a Type-function of the Laplace–Stieltjes transforms convergent in the complex plane, and obtain some formulas about relations between the growth properties of the maximum modulus and the local maximum, which briefly extend some results of Dirichlet series.

Keywords:

• Dirichlet series
• Laplace–Stieltjes transform
• precision order
• Type-function

AMS Subject Classifications:

• 44A10
• 30D15

Acknowledgments

The research was supported by the National Natural Science Foundation of China (Grant No. 11101096 and No. 10901166) and the Guangdong Natural Science Foundation (Grant No. S2012010010376).