Invariant subspaces in certain function spaces on $n$-dimensional Lobachevsky space

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.