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arXiv · 2506.16740

On the rate of convergence of $\mathbb{R}^d$-ergodic averages constructed over a strictly convex set

Ivan Podvigin
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Abstract

For $\mathbb{R}^d$-ergodic means constructed over a strictly convex set, a spectral criterion for homogeneous rates of convergence is obtained. From Hertz's result on the asymptotics of the Fourier transform of the indicator of a strictly convex set, it follows that the rate of convergence does not depend on the specific form of such a set.

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Ivan Podvigin. 2025-06-20. On the rate of convergence of $\mathbb{R}^d$-ergodic averages constructed over a strictly convex set. https://arxiv.org/abs/2506.16740

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