Almost everywhere convergence of convolution powers without finite second moment

Details Almost everywhere convergence of convolution powers without finite second moment Almost everywhere convergence of convolution powers without finite second moment

2010-08-07

arxiv.org/abs/1008.1329v1

Mathematics

Classical Analysis and ODEs

13 pages, to appear in Annales de l Institut Fourier

Scientific paper

We generalize a theorem of Bellow and Calder\'on concerning the a.e.
convergence of the convolution powers $\ds \mu^nf(x)=\sum_{k}\mu^n(k)f(T^k x)$
where $T$ is a measure preserving transformation of a probability space and
$\mu$ is a probability measure on the integers.

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