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

1 Jul 2021, 10:50
30m

Speaker

Konstantin Dyakonov (ICREA and Universitat de Barcelona)

Description

Let $\Lambda$ be a subset of $\mathbb Z_+:=\{0,1,2,\dots\}$, and let $H^\infty(\Lambda)$ denote the space of bounded analytic functions $f$ on the 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 $H^\infty(\Lambda)$.

Primary author

Konstantin Dyakonov (ICREA and Universitat de Barcelona)

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