Geodesic
Differential operators on equivariant vector bundles over symmetric spaces
Electronic Journal of Differential Equations, Tome 2000 (2000).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Generalizing the algebra of motion-invariant differential operators on a symmetric space we study invariant operators on equivariant vector bundles. We show that the eigenequation is equivalent to the corresponding eigenequation with respect to the larger algebra of all invariant operators. We compute the possible eigencharacters and show that for invariant integral operators the eigencharacter is given by the Abel transform. We show that sufficiently regular operators are surjective, i.e. that equations of the form $Df=u$ are solvable for all $u$.
Classification : 43A85, 22E30, 35J45
Keywords: invariant operators 
@article{EJDE_2000__2000__a206,
     author = {Deitmar, Anton},
     title = {Differential operators on equivariant vector bundles over symmetric spaces},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2000},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a206/}
}
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Deitmar, Anton. Differential operators on equivariant vector bundles over symmetric spaces. Electronic Journal of Differential Equations, Tome 2000 (2000). http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a206/