English

Optimal growth of harmonic functions frequently hypercyclic for the partial differentiation operator

Functional Analysis 2019-12-04 v1

Abstract

We solve a problem posed by Blasco, Bonilla and Grosse-Erdmann in 2010 by constructing a harmonic function on RN\mathbb{R}^N, that is frequently hypercyclic with respect to the partial differentiation operator /xk\partial/\partial x_k and which has a minimal growth rate in terms of the average L2L^2-norm on spheres of radius r>0r>0 as rr \to \infty.

Keywords

Cite

@article{arxiv.1708.08764,
  title  = {Optimal growth of harmonic functions frequently hypercyclic for the partial differentiation operator},
  author = {Clifford Gilmore and Eero Saksman and Hans-Olav Tylli},
  journal= {arXiv preprint arXiv:1708.08764},
  year   = {2019}
}
R2 v1 2026-06-22T21:26:35.474Z