no. 2
Almost Everywhere Convergence Of Convolution Powers Without Finite Second Moment
[La convergence presque partout de pouvoirs de convolution sans deuxième moment fini]
Wedrychowicz, Christopher M.1
1 Indiana University South Bend Department of Mathematical Sciences 1700 Mishawaka Ave. South Bend 46634 (USA)
Annales de l'Institut Fourier, Tome 61 (2011) no. 2, pp. 401-415.

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.

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)=∞.

DOI : 10.5802/aif.2618
Classification : 47A35
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$(\alpha )$
Wedrychowicz, Christopher M. 1

1 Indiana University South Bend Department of Mathematical Sciences 1700 Mishawaka Ave. South Bend 46634 (USA) 
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Wedrychowicz, Christopher M. Almost Everywhere Convergence  Of Convolution Powers Without Finite Second Moment. Annales de l'Institut Fourier, Tome 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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