Abstract:
For the convergence rates in the ergodic theorem for unitary actions of locally compact compactly generated abelian groups, we obtain a spectral criterion in terms of the singularity of the spectral measure in a neighborhood of the unit character. It is thus shown that estimates for these rates, as for the classical ergodic theorems for actions of the groups $\Bbb Z$ and $\Bbb R$ studied previously, are necessarily of spectral nature.
Keywords:convergence rates in the ergodic theorem, compactly generated abelian groups.
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