Fourier inversion of invariant integrals on semisimple real Lie groups

Herb, Rebecca A.

doi:10.1090/S0002-9947-1979-0525674-X

Fourier inversion of invariant integrals on semisimple real Lie groups
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by Rebecca A. Herb

Trans. Amer. Math. Soc. 249 (1979), 281-302

DOI: https://doi.org/10.1090/S0002-9947-1979-0525674-X

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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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