Spectral Analysis Implies Spectral Synthesis

TL;DR

This paper demonstrates that spectral analysis inherently leads to spectral synthesis for certain varieties on locally compact Abelian groups, expanding understanding of harmonic analysis in this context.

Contribution

It establishes a link between spectral analysis and spectral synthesis for varieties on specific locally compact Abelian groups, under conditions excluding infinite torsion free subgroups.

Findings

Spectral analysis implies spectral synthesis for the considered varieties.

The result applies to groups with no infinite torsion free discrete subgroups.

Provides a theoretical foundation connecting spectral analysis and synthesis.

Abstract

In this paper we show that spectral analysis implies spectral synthesis for arbitrary varieties on locally compact Abelian groups, which have no discrete subgroup of infinite torsion free rank..