On the Fourier coefficients of powers of a Blaschke factor and strongly annular fonctions

Alexander Borichev, Karine Fouchet, Rachid Zarouf

We compute asymptotic formulas for the $k^{\mathrm{th}}$ Fourier coefficients of $b_{\lambda }^n$, where $b_{\lambda }(z)=\frac{z-\lambda }{1-\lambda z}$ is the Blaschke factor associated to $\lambda \in \mathbb{D}$, $k\in[0,…