随机解析函数的增长率，在线性动力学中的应用

arXiv - MATH - Functional Analysis Pub Date : 2024-09-06 DOI:arxiv-2409.04235

Kevin Agneessens, Karl-G. Grosse-Erdmann

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引用次数: 0

摘要

我们得到了单位盘上随机全函数和随机解析函数的维曼-瓦利隆型不等式，它改进了Erd\H{o}s和R\'enyi的经典结果以及Kuryliak和Skaskiv的最新结果。然后，我们的结果被应用于线性动力学：我们得到了解析函数在某个例外集之外的增长率，这些函数对于任意的混沌加权后移来说经常是超循环的。

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Rate of growth of random analytic functions, with an application to linear dynamics

We obtain Wiman-Valiron type inequalities for random entire functions and for random analytic functions on the unit disk that improve a classical result of Erd\H{o}s and R\'enyi and recent results of Kuryliak and Skaskiv. Our results are then applied to linear dynamics: we obtain rates of growth, outside some exceptional set, for analytic functions that are frequently hypercyclic for an arbitrary chaotic weighted backward shift.

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arXiv - MATH - Functional Analysis

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