K. Fouchet

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20212025

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math.CV2024

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 $ℓ^{\infty}$ -norm of the sequence of the Fourier coefficients of $B^{n}$ as $n$ tends to $\inf…

math.CV2021

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 $k^{th}$ Fourier coefficients of $b_{λ}^{n}$ , where $b_{λ} (z) = \frac{z - λ}{1 - λ z}$ is the Blaschke factor associated to $λ \in D$ , $k\in[0,…