TY - JOUR

T1 - On the support of Plancherel measure

AU - Bernstein, Joseph N.

N1 - Funding Information:
(*) This research was partially supported by NSF.

PY - 1988

Y1 - 1988

N2 - 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.

AB - 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.

KW - Plancherel measure

KW - Tempered representations

KW - polynomial growth

KW - reductive groups

UR - http://www.scopus.com/inward/record.url?scp=0000649145&partnerID=8YFLogxK

U2 - 10.1016/0393-0440(88)90024-1

DO - 10.1016/0393-0440(88)90024-1

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AN - SCOPUS:0000649145

SN - 0393-0440

VL - 5

SP - 663

EP - 710

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

IS - 4

ER -