Discrete series characters and Fourier inversion on semisimple real Lie groups

Herb, Rebecca A.

doi:10.1090/S0002-9947-1983-0690050-7

Discrete series characters and Fourier inversion on semisimple real Lie groups
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by Rebecca A. Herb

Trans. Amer. Math. Soc. 277 (1983), 241-262

DOI: https://doi.org/10.1090/S0002-9947-1983-0690050-7

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Abstract:

Let $G$ be a semisimple real Lie group. Explicit formulas for discrete series characters on noncompact Cartan subgroups are given. These formulas are used to give a simple formula for the Fourier transform of orbital integrals of regular semisimple orbits.

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