Extreme and Exposed Points Arising from Rational Kernels

Abstract

Let ${\beta }_1,...,{\beta }_n$ 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 $\Lambda$