The Distance From a Point to a Compact Convex Set

Abstract

Let $K$ be a compact convex subset of the plane and $\lambda \in \mathbb{C}\backslash K$, then $$ dist(\lambda ,K)=\|(\lambda -N_{\mu})^{-1}\|^{-1},$$ where $\mu$ is the Lebesgue measure concentrated on $K$ and $N_{\mu}$ be the multiplication operator on $L^{2}(\mu)$.