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

Andersen, Nils Byrial

C. R. Acad. Sci., Paris, Sér. I, Math. 327, No. 2, 123-126 (1998).

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

Keywords:

complex connected reductive group; differential operator; symmetric space