Let Hn be the (2n + 1)-dimensional Heisenberg group and K a compact group of automorphisms of Hn such that (K \ltimes 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 R^s homeomorphic to the Gelfand spectrum of the Banach algebra of K -invariant integrable functions on Hn.

Gelfand pairs on the Heisenberg group and Schwartz functions

ASTENGO, FRANCESCA;
2009

Abstract

Let Hn be the (2n + 1)-dimensional Heisenberg group and K a compact group of automorphisms of Hn such that (K \ltimes 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 R^s homeomorphic to the Gelfand spectrum of the Banach algebra of K -invariant integrable functions on Hn.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11567/222648
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 24
  • ???jsp.display-item.citation.isi??? 21
social impact