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Sets of interpolation and small p sets. (English) Zbl 0633.43005

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.
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