Estimates for the Bohr radius of a Faber-Green condenser in the complex plane
We give some upper and lower estimates for the Bohr's radius of a Faber-Green condenser in the complex plane.
math.CV↗
arXiv subjects
Patrice Lassère
Publications and source records attributed to Patrice Lassère.
The Bohr Radius for an Elliptic Condenser
We compute the exact value of the Bohr radius associated to an elliptic condenser of the complex plane and its Faber polynomial basis.
math.CV↗
Bohr's phenomenon on a regular condensator in the complex plane
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 $\sum_n|a_n|\cdot|F_n|_K<1$.
math.CV↗