This article is cited in 6 papers

Invariant subspaces of some function spaces on symmetric spaces. I

S. S. Platonov

Petrozavodsk State University

Abstract: The article describes the construction of closed linear subspaces of some function spaces on the symmetric space $M=\operatorname{SU}(n,1)/U(n)$ that are invariant with respect to the natural quasiregular representation of the group $\operatorname{SU}(n,1)$. The function spaces considered include, in particular, the spaces $C^d(M)$ $(d=0,1,\dots,\infty)$ and spaces of functions of exponential growth on $M$.

MSC: Primary 22E30, 22E46, 43A85; Secondary 43A45, 53C35

Received: 13.05.1994

 English version: Izvestiya: Mathematics, 1995, 59:5, 1007–1050

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