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Summary: On certain Weighted Moving Averages and their
Differentiation analogues
Parthena Avramidou
Abstract. Let (X, , µ, T) be a measure-preserving dynamical system, and
{In} a sequence of intervals of non-negative integers moving to infinity with
increasing cardinality. Rosenblatt and Wierdl constructed optimal weights wn
for the averages of the form
1
wn
X
kIn
f Tk
to converge a.e. in L1. In this paper, we provide modified versions of those
weights to address the question of optimality for more general weighted aver-
ages and their differentiation analogues.
Contents
1. Introduction 1
2. Weighted moving averages and optimal weights 3
3. Weighted differentiation averages and optimal weights 11
Acknowledgments 18
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