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arXiv · 2106.14078

Stability in the Marcinkiewicz theorem

Alexandre Eremenko·Alexander Fryntov
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Abstract

Ostrovskii's generalization of the Marcinkiewicz theorem implies that if an entire characteristic functions of a probability distribution satisfies $\log^+\log|f(z)|=o(|z|),\; z\to\infty,$ and is zero-free then the distribution is normal. We show that under the same growth condition, absence of zeros in a wide vertical strip implies that the distribution is close to a normal one. This generalizes and simplifies a recent result of Michelen and Sahasrabudhe.

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Alexandre Eremenko, Alexander Fryntov. 2021-06-26. Stability in the Marcinkiewicz theorem. https://arxiv.org/abs/2106.14078

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