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Orbital integrals on reductive Lie groups. (Intégrales orbitales sur les groupes de Lie réductifs.) (French) Zbl 0832.22017
The author gives a characterization of orbital integrals (among \(C^\infty\) functions on the regular set of a real reductive Lie group \(G\)) on \(G\) via certain axioms on growth behavior and compactness of support which were previously known for orbital integrals by work of Harish- Chandra. (More precisely, the author works with real points of connected algebraic complex groups defined over \(R\).) He then uses this characterization to prove a scalar Paley-Wiener theorem for \(C^\infty\) functions with compact support on \(G\). He also gives a stable version of his characterization and uses it to extend his Paley-Wiener theorem to homogeneous spaces of complex algebraic groups modulo their real points.

MSC:
22E30 Analysis on real and complex Lie groups
43A80 Analysis on other specific Lie groups
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