A note on the growth of topological Sidon sets
Let \(G\) denote a locally compact abelian group and \(\Lambda\) a subset of the dual group. \(\Lambda\) is called a topological Sidon set if any bounded complex-valued function on \(\Lambda\) may be matched by the restriction to \(\Lambda\) of the Fourier transform of a complex bounded Radon measure \(\mu\) on \(G\). For any such \(\Lambda\) there exist \(c \geq 1\) and a compact subset \(K\) of \(G\) such that the measure \(\mu\) may be assumed to be supported on \(K\) and have norm at most \(c\) times the sup-norm of the associated bounded function on \(\Lambda\). The author gives standard estimates for the number of elements in the intersection of topological Sidon sets with compact convex subsets in \(\mathbb{R}^m\).
scientific article; zbMATH DE number 903362