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

Véronique Fischer, Fulvio Ricci

Research output: Contribution to journalArticle

10 Citations (Scopus)

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) ⋉ N3,2, SO(3)), where N3,2 is the free two-step nilpotent Lie group with three generators. This extends recent results for the Heisenberg group.

Original languageEnglish
Pages (from-to)2143-2168
Number of pages26
JournalAnnales de l'institut Fourier
Volume59
Issue number6
DOIs
Publication statusPublished - 1 Jan 2009

Keywords

  • Gelfand pair
  • Nilpotent lie group
  • Schwartz space

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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