The Growth Of The Generalized Laplace-Stieltjes Transfom

This thesis studies the orders and types of generalized Laplace-Stieltjes transform slow growth by using the basic knowledge of orders and types of Laplace-Stieltjes transform, the infinite order as well as the finite er order of the generalized Laplace-Stieltjes transform in whole planes. The thesis consists of four chapters.The first chapter introduces the definition and associated knowledge of the Dirichlet series and the Laplace-Stieltjes transform order and type.In the second chapter, the thesis kicks around the order and type of the generalized Laplace-Stieltjes transform and the relationship among their maximum modulus, maximum and maximum coefficients on the whole complex plane under the slow growth function.The third chapter mainly talks about how to get two necessary and sufficient conditions of the generalized Laplace-Stieltjes transform infinite order on the whole complex plane by means of introducing type function.In the end, it discusses the relationship between the finite er order p of the entire function represented by the generalized Laplace-Stieltjes transform and An,ωn.