Gelfand transforms of SO(3)-invariant schwartz functions on the free group N3,2

Véronique Fischer; Fulvio Ricci

doi:10.5802/aif.2486

Gelfand transforms of SO(3)-invariant schwartz functions on the free group N_3,2

Véronique Fischer, Fulvio Ricci

Scuola Normale Superiore di Pisa

Research output: Contribution to journal › Article › peer-review

13 Citations (SciVal)

Abstract

The spectrum of a Gelfand pair (K ⋉ N, ), 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) ⋉ 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.

Original language	English
Pages (from-to)	2143-2168
Number of pages	26
Journal	Annales de l'institut Fourier
Volume	59
Issue number	6
DOIs	https://doi.org/10.5802/aif.2486
Publication status	Published - 1 Jan 2009

Keywords

Gelfand pair
Nilpotent lie group
Schwartz space

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology

Access to Document

10.5802/aif.2486

Cite this

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