Asymptotic Location of the Zeros of the Faber Polynomials - Hasson, Maurice; Tabor, Michael (Sarajevo Journal of Mathematics, 2024)
Let $E$ be a compact set of the complex plane containing more than one point whose complement in the extended complex plane is simply connected. Let $ω = φ(z)$ map conformally Ext($E$) into $\vertω\vert>1$ and with $φ(∞)=∞.$ The map $φ(z)$ has the form $$φ(z)=\frac{z}{c}+a_0+\frac{a_{-1}}{ z} +\frac{a_{-2}}{z^2}+ …$$ The Faber polynomials for $E$, $φ_n(z)$, consist of the polynomial part of $φ(z)^n.$ For $ε>0$ given let $$E_ε:=\bigcup_{z\in E}B(z,ε),$$ where $B(z,ε)$ denotes the disk of center $z$ and radius $ε,$ and let $$B_ε:=Br(E_ε).$$ Let $$α:=\inf_{z\inBr(E)}~\left\{θ;~πθ\text{ is the exterior angle of $E$ at }z\right\}.$$ A typical result obtained in this work is the Theorem 3.2. 2000 Mathematics Subject Classification. 31E10, 41A10, 41A29, 41A40