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 -