Extreme and Exposed Points Arising from Rational Kernels

Let ${\beta }_1,\mathrm{.}\mathrm{.}\mathrm{.},{\beta }_n$ be distinct points in the open unit disc in the complex plane, none of which is the origin, and let $H^1$ be the Hardy space. Define a closed convex set in ${\mathbb{C}}^n$ by $\Lambda = { (f(\beta_1),…,f(\beta_n)): f \in H^1, ||f||_1 \le 1 }$. We characterize the extreme and exposed points of $\mathrm{\Lambda }$