Injectivity Sets for Spherical Means on the Heisenberg Group

In this paper we prove that cylinders of the form R = SR × , where SR is the sphere z ∈ n z = R , are injectivity sets for the spherical mean value operator on the Heisenberg group Hn in Lp spaces.W e prove this result as a consequence of a uniqueness theorem for the heat equation associated to the sub-Laplacian. A Hecke–Bochner type identity for the Weyl transform proved by D.Geller and spherical harmonic expansions are the main tools used