Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

Revisiting cyclic elements in growth spaces

Bergqvist, Linus ; Limani, Adem LU and Malman, Bartosz LU (2025) In Annales Fennici Mathematici 50(2). p.761-778
Abstract

We revisit the problem of characterizing cyclic elements for the shift operator in a broad class of radial growth spaces of holomorphic functions on the unit disk, focusing on functions of finite Nevanlinna characteristic. We provide results in the range of Dini regular weights, and in the regime of logarithmic integral divergence. Our proofs are largely constructive and allow for substantial simplifications of earlier works that previously relied on the Carleson Corona Theorem, such as the Korenblum-Roberts Theorem, as well as a more recent result of El-Fallah, Kellay and Seip.

Please use this url to cite or link to this publication:
author
; and
organization
alternative title
En återblick på cykliska element i tillväxtklasser
publishing date
type
Contribution to journal
publication status
published
subject
keywords
30H15, 30H20, 30J15, cyclic vectors, shift operator, Singular inner functions
in
Annales Fennici Mathematici
volume
50
issue
2
pages
18 pages
publisher
Finnish Mathematical Society
external identifiers
  • scopus:105024951384
ISSN
2737-0690
DOI
10.54330/afm.177932
language
English
LU publication?
yes
additional info
Publisher Copyright: © 2025 The Finnish Mathematical Society.
id
eee6ec5f-55c9-4751-add1-c9ca49338fca
date added to LUP
2026-02-24 14:13:49
date last changed
2026-02-24 14:14:58
@article{eee6ec5f-55c9-4751-add1-c9ca49338fca,
  abstract     = {{<p>We revisit the problem of characterizing cyclic elements for the shift operator in a broad class of radial growth spaces of holomorphic functions on the unit disk, focusing on functions of finite Nevanlinna characteristic. We provide results in the range of Dini regular weights, and in the regime of logarithmic integral divergence. Our proofs are largely constructive and allow for substantial simplifications of earlier works that previously relied on the Carleson Corona Theorem, such as the Korenblum-Roberts Theorem, as well as a more recent result of El-Fallah, Kellay and Seip.</p>}},
  author       = {{Bergqvist, Linus and Limani, Adem and Malman, Bartosz}},
  issn         = {{2737-0690}},
  keywords     = {{30H15; 30H20; 30J15; cyclic vectors; shift operator; Singular inner functions}},
  language     = {{eng}},
  month        = {{07}},
  number       = {{2}},
  pages        = {{761--778}},
  publisher    = {{Finnish Mathematical Society}},
  series       = {{Annales Fennici Mathematici}},
  title        = {{Revisiting cyclic elements in growth spaces}},
  url          = {{http://dx.doi.org/10.54330/afm.177932}},
  doi          = {{10.54330/afm.177932}},
  volume       = {{50}},
  year         = {{2025}},
}