Strictly positive definite functions by integral transforms

Abstract

We study the continuity and strict positive definiteness of positive definite functions on quasi-metric spaces given by integral transforms. We apply some of our findings to positive definite functions on the Euclidean space Rm which are given by cosine transforms (m=1) and Fourier–Bessel transforms (m>1). We also apply the results to positive definite functions on a general quasi-metric space realized as extensions of certain real Laplace transforms defined by conditionally negative definite functions on the quasi-metric space itself.