Abstract
Given any continuous increasing function [varphi]:[0,+∞[[arrow right]]0,+∞[ such that [subscript]lim t[arrow right]∞[/subscript] log [varphi](t)/log t=+∞ , we show that there are harmonic functions H on [superscript]...N[/superscript] satisfying the inequality |H(x)|≤[varphi](||x||) for every x∈[superscript]...N[/superscript] , which are universal with respect to translations. This answers positively a problem of D. H. Armitage (2005). The proof combines techniques of Dynamical Systems and Operator Theory, and it does not need any result from Harmonic Analysis.
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