We discuss the geometry of the unit ball -- specifically, the structure of its extreme points (if any) -- in subspaces of $L^1$ and $L^\infty$ on the circle that are formed by functions with prescribed spectral gaps. A similar issue is considered for kernels of Toeplitz operators in $H^\infty$.
Nearly outer functions as extreme points in punctured Hardy spaces
Extreme points of the unit ball of Paley-Wiener space over two symmetric intervals
The Restriction Principle and Commuting Families of Toeplitz Operators on the Unit Ball
![QR code for arXiv:2211.00853 [math.FA]](http://oss.arxitics.com/images/favicon.svg)