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• # Artykuł - szczegóły

## Colloquium Mathematicum

2011 | 124 | 2 | 157-168

## Pointwise convergence for subsequences of weighted averages

EN

### Abstrakty

EN
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.

157-168

wydano
2011

### Twórcy

autor
• Department of Mathematics, University of Wisconsin at Madison, Madison, WI 53706-1388, U.S.A.