An Independent Non-Helson Set of Spectral Synthesis

Using Varopoulos' tensor algebra methods, a brief proof is obtained of the assertion that ifGis a nondiscrete locally compact abelian group, thenGcontains a pair ofK-sets whose sum is an independent non-Helson set of spectral synthesis. IfGis a nondiscrete locally compact abelian I-group, this construction yields an example of a set of bounded spectral synthesis that does not permit bounded synthesis by discrete measures.