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Gelfand pairs on the Heisenberg group and Schwartz functions |
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| Authors: | Francesca Astengo |
| Affiliation: | a Dipartimento di Matematica, Via Dodecaneso 35, 16146 Genova, Italy b Dipartimento di Matematica e Applicazioni, Via Cozzi 53, 20125 Milano, Italy c Scuola Normale Superiore, Piazza dei Cavalieri 7, M 56126 Pisa, Italy |
| Abstract: | Let Hn be the (2n+1)-dimensional Heisenberg group and K a compact group of automorphisms of Hn such that (K?Hn,K) is a Gelfand pair. We prove that the Gelfand transform is a topological isomorphism between the space of K-invariant Schwartz functions on Hn and the space of Schwartz function on a closed subset of Rs homeomorphic to the Gelfand spectrum of the Banach algebra of K-invariant integrable functions on Hn. |
| Keywords: | Gelfand pair Schwartz space Heisenberg group |
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