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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Fourier inversion of invariant integrals on semisimple real Lie groups


Author: Rebecca A. Herb
Journal: Trans. Amer. Math. Soc. 249 (1979), 281-302
MSC: Primary 22E30
MathSciNet review: 525674
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Abstract: Let G be a connected, semisimple real Lie group with finite center. Associated with every regular semisimple element g of G is a tempered invariant distribution $ { \Lambda _g}$ given by an orbital integral. This paper gives an inductive formula for computing the Fourier transform of $ { \Lambda _g}$ in terms of the space of tempered invariant eigendistributions of G.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1979-0525674-X
PII: S 0002-9947(1979)0525674-X
Article copyright: © Copyright 1979 American Mathematical Society