Quadratic Forms in Harmonic Analysis and the Bochner-Eberlein Theorem

Abstract

New characterizations are given of the classes of functions on a locally compact Abelian group which are Fourier-Stieltjes transforms of: bounded measures, nonnegative bounded measures, and integrable functions. These characterizations are all of the same form, viz., that a positive definite Hermitian form dominate a symmetric quadratic form.