Paley-Wiener spaces for real reductive Lie groups

2004/11/16 by Ban, E. P. van den, Schlichtkrull, H.
#22E30 #22E46 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.math/0411363

Abstract

We show that Arthur's Paley-Wiener theorem for K-finite compactly supported smooth functions on a real reductive Lie group G of the Harish-Chandra class can be deduced from the Paley-Wiener theorem we established in the more general setting of a reductive symmetric space. In addition, we formulate an extension of Arthur's theorem to K-finite compactly supported generalized functions (distributions) on G and show that this result follows from the analogous result for reductive symmetric spaces as well.

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