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Fonctions généralisées sur une algèbre de Lie semi-simple réelle. (Generalized functions on a real semisimple Lie algebra). (French) Zbl 0647.22009
Summary: Let \({\mathfrak g}\) be a real semisimple Lie algebra and G a connected Lie group with Lie algebra \({\mathfrak g}\). We construct in a suitable neighbourhood of 0 in \({\mathfrak g}^ a \)G-invariant generalized function, which is an eigenfunction for all G-invariant constant coefficients differential operators on \({\mathfrak g}\). We show on examples how this function occurs in inversion formulas for symmetric spaces of type \(G_ c/G\). We hope that this result extends to all symmetric spaces of this type.

22E60 Lie algebras of Lie groups
53C35 Differential geometry of symmetric spaces
22E30 Analysis on real and complex Lie groups