Positive and Negative Definite Functions on Abelian Semigroups Without Zero

Abstract

The integral representation theorems for positive and negative definite functions obtained so far were all proved under the assumption that the semigroup contained a neutral element, i.e. a “zero” with respect to the additively written semigroup operation. We also saw that some boundedness conditions were necessary for the functions under consideration in order to prove the main representation results.