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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.

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