Paley-Wiener spaces for real reductive Lie groups

Details Paley-Wiener spaces for real reductive Lie groups Paley-Wiener spaces for real reductive Lie groups

2004-11-16

arxiv.org/abs/math/0411363v2

Mathematics

Representation Theory

Latex2e, 28 pages, change of definition of space P^* on p. 17 + minor corrections

Scientific paper

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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