Preimages under linear combinations of iterates of finite Blaschke products

Spyridon Kakaroumpas, Odí Soler i Gibert

Consider a finite Blaschke product $f$ with $f(0)=0$ which is not a rotation and denote by $f^n$ its $n$-th iterate. Given a sequence $\{a_n\}$ of complex numbers, consider the s…