The singular points of analytic functions with finite \(X\)-order defined by Laplace-Stieltjes transformations
Summary: We study the singular points of analytic functions defined by Laplace-Stieltjes transformations which converge on the right half plane, by introducing the concept of \(X\)-order functions. We also confirm the existence of the finite \(X\)-order Borel points of such functions and obtained the extension of the finite \(X\)-order Borel point of two analytic functions defined by two Laplace-Stieltjes transformations convergent on the right half plane. The main results of this paper are improvement of some theorems given by \textit{L. Shang} and \textit{Z. Gao} [Acta Math. Sci., Ser. A, Chin. Ed. 27, No. 6, 1035--1043 (2007; Zbl 1150.30339)].
scientific article; zbMATH DE number 6474243
scientific article