Positive half-characters and the Laplace transformation - Mirotin , A. P. (Ukrains’kyi Matematychnyi Zhurnal, 1992)
It is shown that the image of the conical semigroup S under the natural mapping of it to its second semigroup of positive semicharacters (Ŝ+)^+ is a total subset of the space of continuous functions on Ŝ+ approaching zero at infinity. This allows one to establish a number of properties of the semigroup Ŝ+ and of the Laplace transform of measures on it.