Lacunary polynomials in $L^1$: geometry of the unit sphere

Abstract

Let $\Lambda$ be a finite set of nonnegative integers, and let $\mathcal{P}(\Lambda )$ be the linear hull of the monomials $z^k$ with $k\in \Lambda$, viewed as a subspace of $L^1$ on the unit circle. We characterize the extreme and exposed points of the unit ball in $\mathcal{P}(\Lambda )$.

20 pages

References in corpus (1)

• An extremal problem for functions annihilated by a Toeplitz operator

Cited by in corpus (5)

• Nearly outer functions as extreme points in punctured Hardy spaces
• A Rudin--de Leeuw type theorem for functions with spectral gaps
• Inner functions as strongly extreme points: stability properties
• On geometry of the unit ball of Paley-Wiener space over two symmetric intervals
• Functions with small and large spectra as (non)extreme points in subspaces of $H^{\infty }$