Asymptotic Location of the Zeros of the Faber Polynomials
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 ω>1 and with φ(∞)=∞. The map φ(z) has the form φ(z)=zc+a_0+a_-1 z +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:=_z EB(z,ε), where B(z,ε) denotes the disk of center z and radius ε, and let B_ε:=Br(E_ε). Let α:=_zBr(E) {θ; πθ is the exterior angle of E at z}. A typical result obtained in this work is the Theorem 3.2. 2000 Mathematics Subject Classification. 31E10, 41A10, 41A29, 41A40 , number=2, journal=Sarajevo Journal of Mathematics, author=Hasson, Maurice and Tabor, Michael, year=2024, month=Jun., pages=175–184