|
This article is cited in 1 scientific paper (total in 1 paper)
Research Papers
Functions with small and large spectra as (non)extreme points in subspaces of $H^\infty$
K. M. Dyakonovab a Departament de Matemàtiques i Informàtica, IMUB, BGSMath, Universitat de Barcelona, Gran Via 585, E-08007 Barcelona, Spain
b ICREA, Pg. Lluís Companys 23, E-08010 Barcelona, Spain
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, spectral gaps, lacunary polynomials, extreme points.
Received: 12.10.2021
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
Linking options:
https://www.mathnet.ru/eng/aa1815 https://www.mathnet.ru/eng/aa/v34/i3/p193
|
Statistics & downloads: |
Abstract page: | 317 | Full-text PDF : | 2 | References: | 24 | First page: | 27 |
|