no. 2
Almost Everywhere Convergence Of Convolution Powers Without Finite Second Moment
Wedrychowicz, Christopher M.1
1Indiana University South Bend Department of Mathematical Sciences 1700 Mishawaka Ave. South Bend 46634 (USA)
Annales de l'Institut Fourier, Volume 61 (2011) no. 2, pp. 401-415

Bellow and Calderón proved that the sequence of convolution powers μ n f(x)=∑ k∈ℤ μ n (k)f(T k x) converges a.e, when μ is a strictly aperiodic probability measure on ℤ such that the expectation is zero, E(μ)=0, and the second moment is finite, m 2 (μ)<∞. In this paper we extend this result to cases where m 2 (μ)=∞.

Nous généralisons un théorème de Bellow et Calderón concernant la convergence p.p. de puissances de convolution μ n f(x)=∑ k μ n (k)f(T k x) où T est une transformation préservant la mesure d’un espace de probabilités et μ est une mesure de probabilité sur les nombres entiers.

DOI: 10.5802/aif.2618
Classification: 47A35
Keywords: Convolution powers, a.e convergence, Fourier transform, Lipschitz class Lip$(\alpha )$
Mots-clés : pouvoirs de convulions, convergence p.p, transformée de Fourier, la classe de Lipschitz Lip$(\alpha )$

Wedrychowicz, Christopher M.  1

1 Indiana University South Bend Department of Mathematical Sciences 1700 Mishawaka Ave. South Bend 46634 (USA) 
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
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