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On cyclicity in de Branges-Rovnyak spaces

Bergman, Alex LU (2024) In Indiana University Mathematics Journal 73(4). p.1307-1329
Abstract
We study the problem of characterizing the cyclic vec-
tors in de Branges-Rovnyak spaces. Based on a description of the
invariant subspaces we show that the difficulty lies entirely in un-
derstanding the subspace (aH2)⊥ and give a complete function the-
oretic description of the cyclic vectors in the case dim(aH2)⊥ < ∞.
Incidentally, this implies analogous results for certain generalized
Dirichlet spaces D(μ). Most of our attention is directed to the in-
finite case where we relate the cyclicity problem to describing the
exposed points of H1 and provide several sufficient conditions. A
necessary condition based on the Aleksandrov-Clark measures of b
is also presented.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Indiana University Mathematics Journal
volume
73
issue
4
pages
1307 - 1329
publisher
Indiana University
external identifiers
  • scopus:85208402679
ISSN
0022-2518
DOI
10.1512/iumj.2024.73.60011
language
English
LU publication?
yes
id
fb14256a-8afe-4ee9-bfad-f734bcb52376
alternative location
https://www.iumj.indiana.edu/IUMJ/Preprints/60011.pdf
date added to LUP
2024-01-17 11:11:40
date last changed
2025-02-17 14:48:33
@article{fb14256a-8afe-4ee9-bfad-f734bcb52376,
  abstract     = {{We study the problem of characterizing the cyclic vec-<br/>tors in de Branges-Rovnyak spaces. Based on a description of the<br/>invariant subspaces we show that the difficulty lies entirely in un-<br/>derstanding the subspace (aH2)⊥ and give a complete function the-<br/>oretic description of the cyclic vectors in the case dim(aH2)⊥ &lt; ∞.<br/>Incidentally, this implies analogous results for certain generalized<br/>Dirichlet spaces D(μ). Most of our attention is directed to the in-<br/>finite case where we relate the cyclicity problem to describing the<br/>exposed points of H1 and provide several sufficient conditions. A<br/>necessary condition based on the Aleksandrov-Clark measures of b<br/>is also presented.}},
  author       = {{Bergman, Alex}},
  issn         = {{0022-2518}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{1307--1329}},
  publisher    = {{Indiana University}},
  series       = {{Indiana University Mathematics Journal}},
  title        = {{On cyclicity in de Branges-Rovnyak spaces}},
  url          = {{http://dx.doi.org/10.1512/iumj.2024.73.60011}},
  doi          = {{10.1512/iumj.2024.73.60011}},
  volume       = {{73}},
  year         = {{2024}},
}