Bohr's phenomenon on a regular condensator in the complex plane

Patrice Lassère; Emmanuel Mazzilli

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arXiv · 1008.4215

Bohr's phenomenon on a regular condensator in the complex plane

Patrice Lassère·Emmanuel Mazzilli

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Abstract

We prove the following generalisation of Bohr theorem : let $K\subset\mathbb C$ a continuum, $(F_n)_n$ its Faber polynomials, $Ω_R=\{Φ_K 1)$ the levels sets of the Green function; then there exists $R_0>1$ such that for any $f=\sum_n a_n F_n\in\mathscr O(Ω_{R_0})$ : $f(Ω_{R_0})\subset D(0,1)$ implies $\sum_n|a_n|\cdot|F_n|_K<1$.

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Patrice Lassère, Emmanuel Mazzilli. 2011-03-28. Bohr's phenomenon on a regular condensator in the complex plane. https://arxiv.org/abs/1008.4215

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