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Gelfand transforms of polyradial Schwartz functions on the Heisenberg group |
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| Authors: | Francesca Astengo |
| Institution: | a Dipartimento di Matematica, Università di Genova, Via Dodecaneso 35, 16146 Genova, Italy b Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, Via Cozzi 53, 20125 Milano, Italy c Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy |
| 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. |
| Keywords: | Heisenberg group Gelfand pairs Schwartz functions |
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