Geodesic
Functions with small and large spectra as (non)extreme points in subspaces of $H^\infty$
Algebra i analiz, Tome 34 (2022) no. 3, pp. 193-206

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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 $H^\infty(\Lambda)$.
Keywords: bounded analytic functions, spectral gaps, lacunary polynomials, extreme points. 
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K. M. Dyakonov. Functions with small and large spectra as (non)extreme points in subspaces of $H^\infty$. Algebra i analiz, Tome 34 (2022) no. 3, pp. 193-206. http://geodesic.mathdoc.fr/item/AA_2022_34_3_a8/

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