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A Quick Proof of Harish-Chandra's Plancherel Theorem for Spherical Functions on a Semisimple Lie Group

Jonathan Rosenberg
Proceedings of the American Mathematical Society
Vol. 63, No. 1 (Mar., 1977), pp. 143-149
DOI: 10.2307/2041084
Stable URL: http://www.jstor.org/stable/2041084
Page Count: 7
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A Quick Proof of Harish-Chandra's Plancherel Theorem for Spherical Functions on a Semisimple Lie Group
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Abstract

Some lemmas of S. Helgason and R. Gangolli, originally conceived for proving an analogue of the Paley-Wiener theorem for symmetric spaces, are used to give a quick proof of Harish-Chandra's inversion formula and Plancherel theorem for bi-invariant functions on a semisimple Lie group. The method is elementary in that it does not require introduction of Harish-Chandra's "Schwartz space."

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