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

Konstantin M. Dyakonov

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

Complex Variables 2022-03-18 v2 Classical Analysis and ODEs Functional Analysis

Authors: Konstantin M. Dyakonov

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 $H^\infty(\Lambda)$ .

Keywords

bounded analytic functions hardy space extreme points spectra unit ball

Cite

@article{arxiv.2110.06713,
  title  = {Functions with small and large spectra as (non)extreme points in subspaces of $H^\infty$},
  author = {Konstantin M. Dyakonov},
  journal= {arXiv preprint arXiv:2110.06713},
  year   = {2022}
}

Comments

12 pages; to appear in Algebra i Analiz

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

Abstract

Keywords

Cite

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