Geodesic
Invariant subspaces in some function spaces on symmetric spaces. II
Izvestiya. Mathematics , Tome 62 (1998) no. 2, pp. 339-374.

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Let $G$ be a semisimple connected Lie group with finite centre, $K$ a maximal compact subgroup of $G$, and $M=G/K$ a Riemannian symmetric space of non-compact type. We study the problem of describing the structure of closed linear subspaces in various function spaces on $M$ that are invariant under the quasiregular representation of the group $G$. We consider the case when $M$ is a symplectic symmetric space of rank 1. 
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S. S. Platonov. Invariant subspaces in some function spaces on symmetric spaces. II. Izvestiya. Mathematics , Tome 62 (1998) no. 2, pp. 339-374. http://geodesic.mathdoc.fr/item/IM2_1998_62_2_a5/

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