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 $H^\infty(\Lambda)$.
Supported in part by grant MTM2017-83499-P from El Ministerio de Ciencia e Innovación (Spain) and grant 2017-SGR-358 from AGAUR (Generalitat de Catalunya).
Citation:
K. M. Dyakonov, “Functions with small and large spectra as (non)extreme points in subspaces of $H^\infty$”, Algebra i Analiz, 34:3 (2022), 193–206; St. Petersburg Math. J., 34:3 (2023), 453–462
\Bibitem{Dya22}
\by K.~M.~Dyakonov
\paper Functions with small and large spectra as (non)extreme points in subspaces of $H^\infty$
\jour Algebra i Analiz
\yr 2022
\vol 34
\issue 3
\pages 193--206
\mathnet{http://mi.mathnet.ru/aa1815}
\transl
\jour St. Petersburg Math. J.
\yr 2023
\vol 34
\issue 3
\pages 453--462
\crossref{https://doi.org/10.1090/spmj/1763}
Linking options:
https://www.mathnet.ru/eng/aa1815
https://www.mathnet.ru/eng/aa/v34/i3/p193
This publication is cited in the following 1 articles:
Konstantin M. Dyakonov, “Questions About Extreme Points”, Integr. Equ. Oper. Theory, 95:2 (2023)
Citation in format AMSBIB
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