On measures with small transforms

Abstract

G is a locally compact abelian group whose dual is algebraically ordered, i.e., ordered when considered as a discrete group. Every (Radon) complex measure on G has a unique Lebesgue decomposition: d = d 8 4g(x)dx, where d s is singular and g e L^G). A measure on G is of analytic type if () = 0 for < 0, where is the Fourier-Stieltjes transform of .