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arXiv · 2110.06713

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

Konstantin M. Dyakonov
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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 $H^\infty(\Lambda)$.

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BibTeXRIS

Konstantin M. Dyakonov. 2021-10-13. Functions with small and large spectra as (non)extreme points in subspaces of $H^\infty$. https://arxiv.org/abs/2110.06713

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