A counterexample to discrete spectral synthesis

The purpose of this note is to give a generaltzation of this fact in a non-linear potential theory developed by s.. There is another proof for this result, based

We review the Pontryagin duality theory. A function from G to G' is called a homomorphism if it is continuous and preserves the group operation. B y the category of

Let (~a: hEH~} be an arbitrary collection o/positive numbers indexed over H~. Let 9~ be the directed set consisting of all finite subsets of Hg ordered by inclusion.. We shall

Finally, let us point out that the obtained results are also rather immediate consequences of a quite different method pertaining to the potential theory that

- The LCA group G has the property that every density extends to a bounded linear functional on the space of semi- periodic functions (that is, every density is induced by a measure

Rajagopalan for pointing out the following three errors and for indicating that if one assumes that G is o-compact, then the defective half of the proof of Lemma 2.1 is repaired..

— Using again Lemma 6.3 (ii) the result of Salem [7] and Lemma 6.1 (ii) we see that every group of the from R" X K where K is a compact abelian group, has S-measures provided

Rajagopalan for pointing out the following three errors and for indicating that if one assumes that G is o-compact, then the defective half of the proof of Lemma 2.1 is repaired..