arXiv subjects

Karin Reinhold

Publications and source records attributed to Karin Reinhold.

3 recordsLinked to original sources

arXiv2018

Randomly Perturbed Ergodic Averages

Convergence properties of random ergodic averages have been extensively studied in the literature. In these notes, we exploit a uniform estimate by Cohen \& Cuny who showed convergence of a series along randomly perturbed times for functions in $L^2$ with $\int \max(1,\log (1+|t|)) dμ_f<\infty$. We prove universal pointwise convergence of a class of random averages along randomly perturbed times for $L^2$ functions with $\int \max(1,\log\log(1+|t|)) dμ_f<\infty$. For averages with additional smoothing properties, we obtain a universal variational inequality as well as universal pointwise convergence of a series define by them for all functions in $L^2$.

math.DS↗

arXiv2011

Variation and oscillation inequalities for convolution products

We establish variation and oscillation inequalities for convolution products of probability measures on Z.

math.CA↗

arXiv2011

Almost everywhere convergence of convolution products

Let $(X,\mathcal{B},m,τ)$ be a dynamical system with $\ds (X,\mathcal{B},m)$ a probability space and $\ds τ$ an invertible, measure preserving transformation. The present paper deals with the almost everywhere convergence in $\ds{L}^1(X)$ of a sequence of operators of weighted averages. Almost everywhere convergence follows once we obtain an appropriate maximal estimate and once we provide a dense class where convergence holds almost everywhere. The weights are given by convolution products of members of a sequence of probability measures $\ds\{ν_i\}$ defined on $\ds\mathbb{Z}$. We then exhibit cases of such averages, where convergence fails.

math.CA↗