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Invariant fundamental solutions for invariant differential operators on reductive symmetric spaces of type \(G_\mathbb{C}/G_\mathbb{R}\). (Solutions élémentaires invariantes pour les opérateurs différentiels invariants sur les espaces symétriques réductifs de type \(G_\mathbb{C}/G_\mathbb{R}\).) (French) Zbl 0911.22007
Summary: Let \(G\) be a complex connected reductive group with simply connected derived group. Let \(H\) be a real form of \(G\). Let \(z\) be a \(G\)-invariant differential operator on the reductive symmetric space \(G/H\). We give an explicit sufficient condition for \(z\) to have an invariant fundamental solution on \(G/H\).

MSC:
22E30 Analysis on real and complex Lie groups
43A85 Harmonic analysis on homogeneous spaces
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