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- W2015048939 abstract "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 C R} be a 1-parameter subgroup of hyperbolic translations such that G = KA+K is a Cartan decomposition. Denote by ot the probability measure on G given by ot = mK * 6at * MK, where MK is the normalized Haar measure on K. Let It denote the probablity measure with density vol(Bt)>1XB,(g), where Bt = {g: d(gK, K) < t} and d denotes the canonical G-invariant Riemannian metric on G/K. Let (X, B, A) be a standard Borel probability space on which G acts measurably and ergodically by measure preserving transformations. Let 7r: G -* Iso(LP(X)) be the associated isometric representation, and let 7r(ut) and 7r(!3t) denote the operators canonically associated with Ct and It. Let n(G) = dimR G/K. We prove maximal and pointwise ergodic theorems for the ball averages It on simple real-rank one Lie groups which are analogous to N. Wiener's maximal and pointwise ergodic theorems for ball averages on in. (The general case of ball averages on semisimple groups is completed in [M-N-S].) Our main result is the following:" @default.
- W2015048939 created "2016-06-24" @default.
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- W2015048939 date "2000-06-01" @default.
- W2015048939 modified "2023-09-23" @default.
- W2015048939 title "Analogs of Wiener's ergodic theorems for semisimple Lie groups. II" @default.
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- W2015048939 doi "https://doi.org/10.1215/s0012-7094-00-10323-7" @default.
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