Invariant subspaces of some function spaces on symmetric spaces. I

摘要

The article describes the construction of closed linear subspaces of some function spaces on the symmetric space M SU(n, 1)/U(n) that are invariant with respect to the natural quasiregular representation of the group SU(n, 1). The function spaces considered include, in particular, the spaces Gd(M) (d = 0,1,..., 00) and spaces of functions of exponential growth on M.