A smoother ergodic average
Reinhold, Karin
Illinois J. Math., Tome 44 (2000) no. 4, p. 843-859 / Harvested from Project Euclid
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We study the pointwise behavior of the smoothed out averages $$P_{n}f(x)= \frac{1}{n} \sum_{k=1}^{n} \frac{1}{\epsilon_{k}} \int_{|t| \lt \epsilon_{k}/2} {f(T_{k+t}x)dt},$$ where $T_{t}$ is a measure preserving flow on a probability space. We show that these are good averages in $L^{P}$, $p \gt 1$, if $\epsilon_{k}$ is a convergent sequence or if they are given by stationary random variables. When $p = 1$ the averages are good if $\lim_{k \rightarrow \infty} \epsilon_{k} = \epsilon \gt 0$
Publié le : 2000-12-15
Classification:  47A35,  28D10 
@article{1255984695,
     author = {Reinhold, Karin},
     title = {A smoother ergodic average},
     journal = {Illinois J. Math.},
     volume = {44},
     number = {4},
     year = {2000},
     pages = { 843-859},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1255984695}
}

Reinhold, Karin. A smoother ergodic average. Illinois J. Math., Tome 44 (2000) no. 4, pp.  843-859. http://gdmltest.u-ga.fr/item/1255984695/