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

  • Clifford Gilmore (a1), Eero Saksman (a1) and Hans-Olav Tylli (a1)

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 → ∞.

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

  • Clifford Gilmore (a1), Eero Saksman (a1) and Hans-Olav Tylli (a1)

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