Hervé Queélec

Pluricapacity and approximation numbers of composition operators

For suitable bounded hyperconvex sets $Ω$ in $\mathbb{C}^N$, in particular the ball or the polydisk, we give estimates for the approximation numbers of composition operators $C_ϕ\colon H^2 (Ω) \to H^2 (Ω)$ when $ϕ(Ω)$ is relatively compact in $Ω$, involving the Monge-Ampère capacity of $ϕ(Ω)$.