The growth and value distribution of Laplace-Stieltjes transformations with infinite order in the right half-plane

摘要

By introducing the concept of X U -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 X U -order of these functions have been obtained. We also investigate the value distribution of Laplace-Stieltjes transformations with finite X U -order and obtain the existence of X U -points and X U -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.