This article is cited in 4 papers

Invariant subspaces in some function spaces on symmetric spaces. II

S. S. Platonov

Petrozavodsk State University

Abstract: 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.

MSC: 43A85, 22E46

Received: 25.01.1996

DOI: 10.4213/im178

 English version: Izvestiya: Mathematics, 1998, 62:2, 339–374

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