Geodesic
Invariant subspaces in certain function spaces on $n$-dimensional Lobachevsky space
Sbornik. Mathematics, Tome 65 (1990) no. 2, pp. 439-464 
S. S. Platonov. Invariant subspaces in certain function spaces on $n$-dimensional Lobachevsky space. Sbornik. Mathematics, Tome 65 (1990) no. 2, pp. 439-464. http://geodesic.mathdoc.fr/item/SM_1990_65_2_a8/
@article{SM_1990_65_2_a8,
     author = {S. S. Platonov},
     title = {Invariant subspaces in certain function spaces on $n$-dimensional {Lobachevsky} space},
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     year = {1990},
     volume = {65},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1990_65_2_a8/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $M$ be $n$-dimensional Lobachevsky space, $G$ the connected component of the identity in the group of isometries of $M$. In certain topological vector spaces of functions on $M$ the author obtains a complete description of the closed subspaces invariant under the transformations $f(x)\to f(gx)$, $z\in M$, $g\in G$. Bibliography: 14 titles.

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