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Proceedings of the American Mathematical Society

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A quick proof of Harish-Chandra's Plancherel theorem for spherical functions on a semisimple Lie group


Author: Jonathan Rosenberg
Journal: Proc. Amer. Math. Soc. 63 (1977), 143-149
MSC: Primary 22E30; Secondary 43A90
DOI: https://doi.org/10.1090/S0002-9939-1977-0507231-8
MathSciNet review: 0507231
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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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DOI: https://doi.org/10.1090/S0002-9939-1977-0507231-8
Keywords: Semisimple Lie group, spherical function, inversion formula, Plancherel theorem, c-function
Article copyright: © Copyright 1977 American Mathematical Society