On positive definite measures

In this paper we study the Fourier transform of unbounded measures on a locally compact groupG. After a short introductory section containing background material, especially results established byL. Argabright andJ. Gil De Lamadrid we turn to the main subjects of the paper: first we characterize $$\Re \left( G \right), \mathfrak{J}\left( G \right)$$ andB(G) cones in $$\mathfrak{W}\left( G \right)$$ . After that we establish the subspace $$\mathfrak{W}_\Delta \left( G \right)$$ of $$\mathfrak{W}\left( G \right)$$ which contains $$\mathfrak{W}_p \left( G \right)$$ , the linear span of all positive definite measures.