Geodesic
Averaging theorems for linear operators in compact groups and semigroups
Studia Mathematica, Tome 124 (1997) no. 3, pp. 249-258 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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The Weyl criterion for uniform distribution of a sequence has an especially simple form in compact abelian groups. The authors use this and the structure of compact monothetic groups and semigroups to generalise the convergence, under certain compactness conditions, of the operator averages: $n^{-1} ∑_{k=1}^n T^k → P (n→ ∞)$ where P is a projection associated with the eigenvalue one of T.
DOI : 10.4064/sm-124-3-249-258

G. J. Murphy 1

1 
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G. J.  Murphy. Averaging theorems for linear operators in compact groups and semigroups. Studia Mathematica, Tome 124 (1997) no. 3, pp. 249-258. doi: 10.4064/sm-124-3-249-258

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