This article is cited in 8 papers

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

S. S. Platonov


Abstract: 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.

UDC: 517.954

MSC: Primary 43A15; Secondary 46A12

Received: 20.07.1987

 English version: Mathematics of the USSR-Sbornik, 1990, 65:2, 439–464

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