Note on approximation in locally compact Abelian groups (Q1122079)

Let G be a LCA group and V an open neighborhood of 0 in G. Let \(p\in [1,\infty)\). For \(f\in L^ p(G)\), set \(w^*(p,f,V)=\sup \{\| \tau_ af+\tau_{-a}f-2f\|_ p:a\in V\},\) where \(\tau_ af(x)=f(x-a)\). The author examines a connection between \(w^*\) and the degree of approximation of f by functions with certain compact spectra.