Pointwise convergence for subsequences of weighted averages

Patrick LaVictoire. "Pointwise convergence for subsequences of weighted averages." Colloquium Mathematicae 124.2 (2011): 157-168. <http://eudml.org/doc/284036>.

@article{PatrickLaVictoire2011,
abstract = {We prove that if μₙ are probability measures on ℤ such that μ̂ₙ converges to 0 uniformly on every compact subset of (0,1), then there exists a subsequence $\{n_\{k\}\}$ such that the weighted ergodic averages corresponding to $μ_\{n_\{k\}\}$ satisfy a pointwise ergodic theorem in L¹. We further discuss the relationship between Fourier decay and pointwise ergodic theorems for subsequences, considering in particular the averages along n² + ⌊ρ(n)⌋ for a slowly growing function ρ. Under some monotonicity assumptions, the rate of growth of ρ’(x) determines the existence of a “good” subsequence of these averages.},
author = {Patrick LaVictoire},
journal = {Colloquium Mathematicae},
keywords = {subsequence averages; ergodic theorem; weighted averages; good sequences},
language = {eng},
number = {2},
pages = {157-168},
title = {Pointwise convergence for subsequences of weighted averages},
url = {http://eudml.org/doc/284036},
volume = {124},
year = {2011},
}

TY - JOUR
AU - Patrick LaVictoire
TI - Pointwise convergence for subsequences of weighted averages
JO - Colloquium Mathematicae
PY - 2011
VL - 124
IS - 2
SP - 157
EP - 168
AB - We prove that if μₙ are probability measures on ℤ such that μ̂ₙ converges to 0 uniformly on every compact subset of (0,1), then there exists a subsequence ${n_{k}}$ such that the weighted ergodic averages corresponding to $μ_{n_{k}}$ satisfy a pointwise ergodic theorem in L¹. We further discuss the relationship between Fourier decay and pointwise ergodic theorems for subsequences, considering in particular the averages along n² + ⌊ρ(n)⌋ for a slowly growing function ρ. Under some monotonicity assumptions, the rate of growth of ρ’(x) determines the existence of a “good” subsequence of these averages.
LA - eng
KW - subsequence averages; ergodic theorem; weighted averages; good sequences
UR - http://eudml.org/doc/284036
ER -