Density of translates in weighted \(L^{p}\) spaces on locally compact groups (Q2364421)

Let \(G\) be a locally compact group and let \(1\leq p < \infty\). For a subset \(S\subseteq G\), the authors give a characterization for existence of a vector \(f\) in the weighted \(L^p\)-space \(L^p ( G, \omega ) = \{ h: \int | h \omega |^p < \infty \}\) such that the set of all left translations of the vector \(f\) is dense in \(L^p ( G, \omega )\).