From the author’s abstract: “The author proves an \(L^ 2\)-version of Wiener’s general Tauberian theorem on a locally compact group G with Haar measure dg. The closure of the linear span of left and right translates of a function \(\xi \in L^ 2(G,dg)\) is all of \(L^ 2\), if “in the decomposition of \(L^ 2(G)\) over the centre of the von Neumann algebra, generated by left G-translations, almost all components of \(\xi\) are nonzero”.”