\(L^ 2\) version of Wiener’s Tauberian theorem. (English. Abridged French version) Zbl 0703.43006
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”.”
Reviewer: Wolfgang Schwarz (Frankfurt / Main)
MSC:
43A70 | Analysis on specific locally compact and other abelian groups |
40E05 | Tauberian theorems |
43A15 | \(L^p\)-spaces and other function spaces on groups, semigroups, etc. |
46L10 | General theory of von Neumann algebras |