On the failure of spectral synthesis for compact semisimple Lie groups

Christopher Meaney*

*Corresponding author for this work

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Let G be a compact connected semisimple Lie group with Lie algebra g. We show that the conjugacy class of a regular element of G is not a set of synthesis for the Fourier algebra of G. Similarly, the Ad(G)-orbit of a regular element of g is not a set of synthesis for the algebra of Fourier transforms on g. In proving this latter result we demonstrate a regularity property of Ad-invariant Fourier transforms, analogous to the differentiability of radial Fourier transforms.

Original languageEnglish
Pages (from-to)43-57
Number of pages15
JournalJournal of Functional Analysis
Volume48
Issue number1
DOIs
Publication statusPublished - 1982
Externally publishedYes

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