Nilpotent Lie groups: Fourier inversion and prime ideals

Ying-Fen Lin, Jean Ludwig, Carine Molitor-Braun

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Abstract

We establish a Fourier inversion theorem for general connected, simply connected nilpotent Lie groups G= \exp(\g) by showing that operator fields defined on suitable sub-manifolds of g^∗ are images of Schwartz functions under the Fourier transform. As an application of this result, we provide a complete characterisation of a large class of invariant prime closed two-sided ideals of L^1(G) as kernels of sets of irreducible representations of G.
Original languageEnglish
Pages (from-to)345-376
Number of pages32
JournalJournal of Fourier Analysis and Applications
Volume25
Issue number2
Early online date01 Dec 2017
DOIs
Publication statusPublished - 01 Apr 2019

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