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.
Astengo, F., DI BLASIO, B., Ricci, F. (2007). Gelfand transforms of polyradial Schwartz functions on the Heisenberg group. JOURNAL OF FUNCTIONAL ANALYSIS, 251(2), 772-791 [10.1016/j.jfa.2007.06.010].
Gelfand transforms of polyradial Schwartz functions on the Heisenberg group
DI BLASIO, BIANCA;
2007
Abstract
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.
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