An Independent Non-Helson Set of Spectral Synthesis

Using Varopoulos’ tensor algebra methods, a brief proof is obtained of the assertion that if G is a nondiscrete locally compact abelian group, then G contains a pair of K-sets whose sum is an independent non-Helson set of spectral synthesis. If G is 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.