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

Clifford Gilmore, Eero Saksman, Hans-Olav Tylli

Type: Article

Publication Date: 2019-01-18

Citations: 6

DOI: https://doi.org/10.1017/prm.2018.82

Abstract

Abstract We solve a problem posed by Blasco, Bonilla and Grosse-Erdmann in 2010 by constructing a harmonic function on ℝ N , that is frequently hypercyclic with respect to the partial differentiation operator ∂/∂ x k and which has a minimal growth rate in terms of the average L 2 -norm on spheres of radius r > 0 as r → ∞.

Locations

Proceedings of the Royal Society of Edinburgh Section A Mathematics - View
arXiv (Cornell University) - View - PDF
DataCite API - View

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Works Cited by This (8)

Action	Title	Year	Authors
+	Harmonic Function Theory	1992	Sheldon Axler Paul Bourdon Wade Ramey
+	Frequently hypercyclic operators	2006	Frédéric Bayart Sophie Grivaux
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+ PDF Chat	Chaos of the Differentiation Operator on Weighted Banach Spaces of Entire Functions	2011	José Bonet A. Bonilla
+	Optimal growth of entire functions frequently hypercyclic for the differentiation operator	2012	David Drasin Eero Saksman
+	Harmonic Analogues of G. R. MacLane's Universal Functions, II	1998	M. P. Aldred D. H. Armitage
+	Harmonic Analogues of G. R. Maclane's Universal Functions	1998	M. P. Aldred D. H. Armitage
+	Dynamics of Linear Operators	2009	Frédéric Bayart Étienne Matheron