Rate of growth of random analytic functions, with an application to linear dynamics
Complex Variables
2024-09-09 v1 Functional Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.2409.04235,
title = {Rate of growth of random analytic functions, with an application to linear dynamics},
author = {Kevin Agneessens and Karl-G. Grosse-Erdmann},
journal= {arXiv preprint arXiv:2409.04235},
year = {2024}
}