1.1. Measurable actions. Let us begin by recalling some well-known facts which are needed
in order to establish the existence of the operators which are the subject of the present …

Consider the following generalization of the foregoing setup. Let G be a connected Lie
group G, and let K be a compact subgroup. Assume there exists a G-invariant Riemannian …

THEOREM C. For G SO (n, 1), n>/3, at is apointwise ergodicfamily in L2. To prove Theorem
1--namely, pointwise convergence of z (trt) f (x) for f LP--it is enough, using standard …

Let X be a compact metrizable space,~(X) its G-algebra of Borel sets, and let T be a
homeomorphism of X. We denote for a Borel measure# on X by T/2 the measure that is …

The basic idea in using group representations for questions of ergodicity is the following. If G
acts ergodically on (S, p), where p is a finite G-invariant measure, then there is a naturally …

In this paper we investigate the validity of the individual ergodic theorem for general non-
abelian groups. The main result is that this, as well as the dominated ergodic theorem, hold …

Let B be any group or semi-group of linear operators T, on a Banach space E. By a (mean)"
ergodic theorem," we mean a theorem asserting the convergence of the means E XkxT, of …

I. Introduction. In their generalization of F. and M. Riesz'Theorem to compact abelian groups
with ordered duals [1], K. deLeeuw and I. Glicksberg introduced analytic measures and …

Let G be a connected finite-center simple Lie group of real rank one, and let K be a maximal
compact subgroup of G. Let A={at I t CR} be a 1-parameter subgroup of hyperbolic …

1. Introduction. The main object of the present paper is to describe a generalization of some
aspects of the classical von Neumann-Krylov-Bogoljubov theory of the decomposition of a …