A proof of Kahane's conjecture in the Wiener algebra

Przemysław Ohrysko

We prove Kahane's conjecture: if a continuous unimodular function $F$ on the circle satisfies $\Vert F^n{\Vert }_{A(\mathbb{T})}=o(\log |n|)$ as $|n|\to \infty$, $n\in \mathbb{Z}$, then $F(x)=e…