H-Regular Borel measures on locally compact abelian groups

TL;DR

This paper characterizes H-regular measures on the dual group of a locally compact abelian group and provides a Wold type decomposition, advancing the understanding of measure classes in harmonic analysis.

Contribution

It introduces a new characterization of H-regular measures and establishes a Wold type decomposition for these measures in the context of LCA groups.

Findings

Characterization of H-regular measures on dual groups

Wold type decomposition for H-regular measures

Extension of prediction theory concepts to LCA groups

Abstract

Let $G$ be an LCA group, $H$ a closed subgroup, $\varGamma$ the dual group of $G$. In accordance with analogous notions in prediction theory the classes of $H$-regular and $H$-singular Borel measures on $\Gamma$ are defined. A characterization of $H$-regular measures is given and a Wold type decomposition is obtained.