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

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 $\hat{f}(k)$ 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 $H^{\infty }(\Lambda )$.

12 pages; to appear in Algebra i Analiz

References in corpus (3)

• Lacunary polynomials in $L^1$: geometry of the unit sphere
• Nearly outer functions as extreme points in punctured Hardy spaces
• A Rudin--de Leeuw type theorem for functions with spectral gaps