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

Patrice Lassère, Emmanuel Mazzilli

We prove the following generalisation of Bohr theorem : let $K\subset \mathbb{C}$ a continuum, $(F_n{)}_n$ its Faber polynomials, ${\Omega }_R=\{{\Phi }_K<R\},(R>1)$ the levels sets of the Green fu…