Functions with small and large spectra as (non)extreme points in subspaces of $H^\infty$ (2110.06713v2)

Abstract: Given a subset $\Lambda$ of $\mathbb Z_+:={0,1,2,\dots}$, let $H^\infty(\Lambda)$ denote the space of bounded analytic functions $f$ on the unit disk whose coefficients $\widehat f(k)$ vanish for $k\notin\Lambda$. Assuming that either $\Lambda$ or $\mathbb Z_+\setminus\Lambda$ is finite, we determine the extreme points of the unit ball in $H^\infty(\Lambda)$.