On coanalytic families of sets in harmonic analysis
Let \(\Gamma\) be a countably infinite Abelian discrete group, and G its compact dual group. A subset \(\Lambda\) of \(\Gamma\) is called a Rosenthal set if any function in \(L^{\infty}(G)\) whose Fourier transform vanishes outside \(\Lambda\) belongs to C(G). It is shown that the family of Rosenthal subsets of \(\Gamma\) is a coanalytic non Borel subset of \(2^{\Gamma}\).
scientific article; zbMATH DE number 4153184