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

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

2010-08-25

arxiv.org/abs/1008.4215v4

Mathematics

Complex Variables

12 pages - V3 - English version, to appear in Computional Methods and Function Theory

Scientific paper

We prove the following generalisation of Bohr theorem : let $K\subset\mathbb
C$ a continuum, $(F_n)_n$ its Faber polynomials, $\Omega_R=\{\Phi_K1)$
the levels sets of the Green function; then there exists $R_0>1$ such that for
any $f=\sum_n a_n F_n\in\mathscr O(\Omega_{R_0})$ : $f(\Omega_{R_0})\subset
D(0,1)$ implies $\sum_n|a_n|\cdot|F_n|_K<1$.

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