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Optimal growth of harmonic functions frequently hypercyclic for the partial differentiation operator
Published online by Cambridge University Press: 18 January 2019
Abstract
We solve a problem posed by Blasco, Bonilla and Grosse-Erdmann in 2010 by constructing a harmonic function on ℝN, that is frequently hypercyclic with respect to the partial differentiation operator ∂/∂xk and which has a minimal growth rate in terms of the average L2-norm on spheres of radius r > 0 as r → ∞.
MSC classification
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 149 , Issue 6 , December 2019 , pp. 1577 - 1594
- Copyright
- Copyright © Royal Society of Edinburgh 2019
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