On the Fourier coefficients of powers of a finite Blaschke product

Alexander Borichev, Karine Fouchet, Rachid Zarouf

Given a finite Blaschke product $B$ we prove asymptotically sharp estimates on the ${\ell }^{\infty }$-norm of the sequence of the Fourier coefficients of $B^n$ as $n$ tends to $\inf…