Almost Everywhere Convergence Of Convolution Powers Without Finite Second Moment
Christopher M. Wedrychowicz[1]
- [1] Indiana University South Bend Department of Mathematical Sciences 1700 Mishawaka Ave. South Bend 46634 (USA)
Annales de l’institut Fourier (2011)
- Volume: 61, Issue: 2, page 401-415
- ISSN: 0373-0956
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topWedrychowicz, Christopher M.. "Almost Everywhere Convergence Of Convolution Powers Without Finite Second Moment." Annales de l’institut Fourier 61.2 (2011): 401-415. <http://eudml.org/doc/219719>.
@article{Wedrychowicz2011,
abstract = {Bellow and Calderón proved that the sequence of convolution powers $ \mu _n f(x)=\sum _\{k\in \mathbb\{Z\}\}\mu ^n(k)f(T^k x)$ converges a.e, when $\mu $ is a strictly aperiodic probability measure on $\mathbb\{Z\}$ such that the expectation is zero, $ E(\mu )=0$, and the second moment is finite, $ m_2(\mu )<\infty $. In this paper we extend this result to cases where $ m_2(\mu )=\infty $.},
affiliation = {Indiana University South Bend Department of Mathematical Sciences 1700 Mishawaka Ave. South Bend 46634 (USA)},
author = {Wedrychowicz, Christopher M.},
journal = {Annales de l’institut Fourier},
keywords = {Convolution powers; a.e convergence; Fourier transform; Lipschitz class Lip$(\alpha )$; convolution powers; Lipschitz class },
language = {eng},
number = {2},
pages = {401-415},
publisher = {Association des Annales de l’institut Fourier},
title = {Almost Everywhere Convergence Of Convolution Powers Without Finite Second Moment},
url = {http://eudml.org/doc/219719},
volume = {61},
year = {2011},
}
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
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 2
SP - 401
EP - 415
AB - Bellow and Calderón proved that the sequence of convolution powers $ \mu _n f(x)=\sum _{k\in \mathbb{Z}}\mu ^n(k)f(T^k x)$ converges a.e, when $\mu $ is a strictly aperiodic probability measure on $\mathbb{Z}$ such that the expectation is zero, $ E(\mu )=0$, and the second moment is finite, $ m_2(\mu )<\infty $. In this paper we extend this result to cases where $ m_2(\mu )=\infty $.
LA - eng
KW - Convolution powers; a.e convergence; Fourier transform; Lipschitz class Lip$(\alpha )$; convolution powers; Lipschitz class
UR - http://eudml.org/doc/219719
ER -
References
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