2010/08/25 by Patrice Lassère, Lassère, Patrice, Emmanuel Mazzilli +1
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #math.CV
paper · pdf · doi:10.48550/arxiv.1008.4215
12 pages - V3 - English version, to appear in Computional Methods and Function Theory
arxiv created 2011/03/28 · arxiv updated 2011/03/29
We prove the following generalisation of Bohr theorem : let K⊂\mathbb C a continuum, (Fn)n its Faber polynomials, ΩR=\ΦK<R\, (R>1) the levels sets of the Green function; then there exists R0>1 such that for any f=∑n an Fn∈\mathscr O(ΩR0) : f(ΩR0)⊂ D(0,1) implies ∑n|an|⋅|Fn|K<1.