Let Γ be an LCA group and A(Γ) the corresponding Fourier algebra. We show that if K ⊆ Γ is an n-point set, then √ n/2 ≤ αΓ(K) ≤ √ n where αΓ(K) is the infimum of the norms of all linear extension operators from C0(K) to A(Γ). The lower bound implies that if K is an infinite closed subset of Γ, then there does not exist a bounded linear extension operator from C0(K) to A(Γ).

Abstract Let G be a locally compact abelian group. A translation-invariant subspace in L 1 ( G ) may or may not be complemented depending on the structure of its hull in Ĝ. Techniques for deciding… Expand

In the late 1950s, many of the more refined aspects of Fourier analysis were transferred from their original settings (the unit circle, the integers, the real line) to arbitrary locally compact… Expand