In Koenigs' footsteps: Diagonalization of composition operators

Wolfgang Arendt, Benjamin Célariès, Isabelle Chalendar

Let $\phi :\mathbb{D}\to \mathbb{D}$ be a holomorphic map with a fixed point $\alpha \in \mathbb{D}$ such that $0\le |{\phi }^{\prime }(\alpha )|<1$. We show that the spectrum of the composition operator $C_{\phi }$…