On the support of Plancherel measure

Joseph N. Bernstein*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Let G be a real reductive group. As follows from Plancherel formula for G, proved by Harish-Chandra, only tempered representations of G contribute to the decomposition of the regular representation in L2(G). We give a simple direct proof of this result, based on Gelfand-Kostyuchenko method. We also prove similar results for representations, which appear in the decomposition of L2(X), where X is a homogeneous G-space of polynomial growth. (See precise definition in 3.5). Important examples of such space X are semisimple symmetric spaces and quotient of G by arithmetic subgroups.

Original languageEnglish
Pages (from-to)663-710
Number of pages48
JournalJournal of Geometry and Physics
Issue number4
StatePublished - 1988
Externally publishedYes


  • Plancherel measure
  • Tempered representations
  • polynomial growth
  • reductive groups


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