On an analogue of the Wiener-Tauberian theorem for symmetric spaces of the noncompact type
Let X be a symmetric space of the non-compact type and G the connected component of the group of isometries of X. Let K be a fixed maximal compact subgroup of G. Let f be a (left) K-finite integrable function on X. We consider conditions under which \(Sp=\{^ gf:\) \(g\in G\}\) is dense in \(L^ 1(X)\), in terms of the ``Fourier transform'' of f. This continues earlier work on this kind of problem by L. Ehrenpreis and F. I. Mautner, R. Krier and also by the author.
scientific article; zbMATH DE number 4021849