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.
Annales de l'Institut Fourier, Tome 61 (2011), p. 401-415 / Harvested from Numdam
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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)=∞.

Publié le : 2011-01-01
DOI : https://doi.org/10.5802/aif.2618
Classification:  47A35
Mots clés: pouvoirs de convulions, convergence p.p, transformée de Fourier, la classe de Lipschitz Lip(α) 
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     author = {Wedrychowicz, Christopher M.},
     title = {Almost Everywhere Convergence  Of Convolution Powers Without Finite Second Moment},
     journal = {Annales de l'Institut Fourier},
     volume = {61},
     year = {2011},
     pages = {401-415},
     doi = {10.5802/aif.2618},
     zbl = {1242.47010},
     mrnumber = {2895062},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2011__61_2_401_0}
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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) pp. 401-415. doi : 10.5802/aif.2618. http://gdmltest.u-ga.fr/item/AIF_2011__61_2_401_0/

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