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MR2075916 (2005f:22025) 22E50 (20G25 22E35)
Kim, JuLee (1IASPSM)
Dual blobs and Plancherel formulas. (English, French summaries)
Bull. Soc. Math. France 132 (2004), no. 1, 5580.
Let k be a padic field, G the group of krational points of a connected reductive group defined
over k, and let g be its Lie algebra. Let G denote the tempered dual of G. From HarishChandra's
Plancherel formulas on g and G, one gets the equality
g
f(X)dX =
G
(f log)d,
for any f C
c (g) supported in a sufficiently small neighbourhood of zero. Here is the
character of , and f is the Fourier transform of f. The main theorem of the paper under review
refines the above equality by establishing an equality between spectral decomposition factors of
each side.
