Bellow and Calderón proved that the sequence of convolution powers converges a.e, when is a strictly aperiodic probability measure on such that the expectation is zero, , and the second moment is finite, . In this paper we extend this result to cases where .
Nous généralisons un théorème de Bellow et Calderón concernant la convergence p.p. de puissances de convolution où est une transformation préservant la mesure d’un espace de probabilités et est une mesure de probabilité sur les nombres entiers.
Keywords: Convolution powers, a.e convergence, Fourier transform, Lipschitz class Lip$(\alpha )$
Mot clés : pouvoirs de convulions, convergence p.p, transformée de Fourier, la classe de Lipschitz Lip$(\alpha )$
@article{AIF_2011__61_2_401_0, author = {Wedrychowicz, Christopher M.}, title = {Almost {Everywhere} {Convergence} {Of} {Convolution} {Powers} {Without} {Finite} {Second} {Moment}}, journal = {Annales de l'Institut Fourier}, pages = {401--415}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {61}, number = {2}, year = {2011}, doi = {10.5802/aif.2618}, zbl = {1242.47010}, mrnumber = {2895062}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2618/} }
TY - JOUR AU - Wedrychowicz, Christopher M. TI - Almost Everywhere Convergence Of Convolution Powers Without Finite Second Moment JO - Annales de l'Institut Fourier PY - 2011 SP - 401 EP - 415 VL - 61 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2618/ DO - 10.5802/aif.2618 LA - en ID - AIF_2011__61_2_401_0 ER -
%0 Journal Article %A Wedrychowicz, Christopher M. %T Almost Everywhere Convergence Of Convolution Powers Without Finite Second Moment %J Annales de l'Institut Fourier %D 2011 %P 401-415 %V 61 %N 2 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2618/ %R 10.5802/aif.2618 %G en %F AIF_2011__61_2_401_0
Wedrychowicz, Christopher M. Almost Everywhere Convergence Of Convolution Powers Without Finite Second Moment. Annales de l'Institut Fourier, Volume 61 (2011) no. 2, pp. 401-415. doi : 10.5802/aif.2618. http://www.numdam.org/articles/10.5802/aif.2618/
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