Gelfand transforms of polyradial Schwartz functions on the Heisenberg group

We prove that the Gelfand transform is a topological isomorphism between the space of polyradial Schwartz functions on the Heisenberg group and the space of Schwartz functions on the Heisenberg brush. We obtain analogous results for radial Schwartz functions on Heisenberg type groups. © 2007 Elsevier Inc. All rights reserved.