Let Hnbe the (2n+1)-dimensional Heisenberg group and Ka compact group of automorphisms of Hnsuch 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 Hnand the space of Schwartz function on a closed subset of Rshomeomorphic to the Gelfand spectrum of the Banach algebra of K-invariant integrable functions on Hn.

Astengo, F., DI BLASIO, B., & Ricci, F. (2009). Gelfand pairs on the Heisenberg group and Schwartz functions. JOURNAL OF FUNCTIONAL ANALYSIS, 256(5), 1565-1587 [10.1016/j.jfa.2008.10.008].

Gelfand pairs on the Heisenberg group and Schwartz functions

DI BLASIO, BIANCA;
2009

Abstract

Let Hnbe the (2n+1)-dimensional Heisenberg group and Ka compact group of automorphisms of Hnsuch 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 Hnand the space of Schwartz function on a closed subset of Rshomeomorphic to the Gelfand spectrum of the Banach algebra of K-invariant integrable functions on Hn.
Articolo in rivista - Articolo scientifico
Gelfand pairs, Schwartz functions,
English
1565
1587
Astengo, F., DI BLASIO, B., & Ricci, F. (2009). Gelfand pairs on the Heisenberg group and Schwartz functions. JOURNAL OF FUNCTIONAL ANALYSIS, 256(5), 1565-1587 [10.1016/j.jfa.2008.10.008].
Astengo, F; DI BLASIO, B; Ricci, F
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/5509
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