JH-Regular Borel measures on locally compact abelian groups

Abstract

Let G be an LCA group, H a closed subgroup, Γ the dual group of G. In accordance with analogous notions in prediction theory the classes of J_H-regular and J_H-singular Borel measures on Γ are defined. A characterization of J_H-regular measures is given anda Wold type decomposition is obtained. Relations to the Whittaker-Shannon-Kotel´nikov theorem are discussed.