On an analogue of the Wiener Tauberian theorem for symmetric spaces of the noncompact type

Abstract

Let X be a symmetric space and G the connected component of the group of isometries of X. If ƒ ∈ L¹(X), we consider conditions under which Sp{^gƒ:g ∈ G} is dense in L¹(X) in terms of the "Fourier transform" of ƒ. This continues earlier work on this kind of problem by L. Ehrenpreis and F. I. Mautner, R. Krier and the author.