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arXiv · 1109.0488

Optimal growth of frequently hypercyclic entire functions

David Drasin·Eero Saksman
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Abstract

We solve a problem posed by A. Bonilla and K.-G. Grosse-Erdmann by constructing an entire function $f$ that is frequently hypercyclic with respect to the differentiation operator, and satisfies $M_f(r)\leq\displaystyle ce^r r^{-1/4}$, where $c>0$ be chosen arbirarily small. The obtained growth rate is sharp. We also obtain optimal results for the growth when measured in terms of average $L^p$-norms. Among other things, the proof applies Rudin-Shapiro polynomials and heat kernel estimates.

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David Drasin, Eero Saksman. 2011-09-02. Optimal growth of frequently hypercyclic entire functions. https://arxiv.org/abs/1109.0488

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