Pigno, Louis Sets of interpolation and small p sets. (English) Zbl 0633.43005 Colloq. Math. 51, 277-279 (1987). Let G be a compact abelian group with dual group \(\Gamma\), measure algebra \(M(G)\supset L_ 1(G)\), and discrete measures \(M_ d(G)\). A subset \(S\subset \Gamma\) is called a small p set if the p-fold convolution \(\mu^ p\in L_ 1(G)\) whenever supp \({\hat \mu}\subset S\). Here is the main Theorem. Let S be a small p set and let \(A\subset \Gamma\) satisfy \(L_ 1(G)^{\wedge}|_ A\subset M_ d(G)^{\wedge}|_ A\). Then \(S\cup A\) is a small \(p^ 2\) set. Reviewer: P.Milnes MSC: 43A25 Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups 43A46 Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.) 43A20 \(L^1\)-algebras on groups, semigroups, etc. Keywords:compact abelian group; dual group; measure algebra; convolution; small p set PDFBibTeX XMLCite \textit{L. Pigno}, Colloq. Math. 51, 277--279 (1987; Zbl 0633.43005) Full Text: DOI