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.
Articolo in rivista - Articolo scientifico
Heisenberg group; Gelfand pairs; Schwartz functions
English
2007
251
2
772
791
none
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].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/792
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