ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

7. Lie Groups and Lie Algebras

1991 MS Classification: 22, 43, 53 Platonov, Sergei S. , Invariant subspaces of some function spaces on symmetric spaces Let G be a connected, non–compact, semi–simple Lie group with finite centre, K a maximal compact subgroup of G, and M = G/K a Riemannian symmetric space of noncompact type. Let F be a locally convex space of functions on M, and π(g) : f(x) ↦ F (g^{−1}x) the quasiregular representation of the group G on the space F. A linear subspace H ⊂ F is called an invariant subspace if it is closed and π-invariant. We describe the construction of invariant subspaces of some function spaces in case when M is a Riemannian symmetric space of rank 1. The function spaces F considered include, in particular, the spaces C^{d}(M) (d = 0, 1, …, ∞) and spaces of functions of exponential growth on M. Reference: S. Platonov, Invariant subspaces of some function spaces on symmetric spaces. I. Izv. Math. 59 (1995), 1007–1050.