Gelfand transforms of SO(3)-invariant Schwartz functions on the free group N_{3,2}

dc.creatorFischer, Veronique
dc.creatorRicci, Fulvio
dc.date2008-09-11
dc.date.accessioned2026-07-07T10:02:14Z
dc.date.available2026-07-07T10:02:14Z
dc.descriptionThe spectrum of a Gelfand pair $(K\ltimes N, K)$, where $N$ is a nilpotent group, can be embedded in a Euclidean space. We prove that in general, the Schwartz functions on the spectrum are the Gelfand transforms of Schwartz $K$-invariant functions on $N$. We also show the converse in the case of the Gelfand pair $(SO(3)\ltimes N_{3,2}, SO(3))$, where $N_{3,2}$ is the free two-step nilpotent Lie group with three generators. This extends recent results for the Heisenberg group.
dc.description28 pages
dc.identifierhttps://arxiv.org/abs/0809.1952
dc.identifierhttp://arxiv.org/abs/0809.1952
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/168899
dc.subjectFunctional Analysis
dc.subjectClassical Analysis and ODEs
dc.subject43A80; 22E25
dc.titleGelfand transforms of SO(3)-invariant Schwartz functions on the free group N_{3,2}
dc.typetext

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