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Hilbert spaces of analytic functions with a contractive backward shift

Aleman, Alexandru LU and Malman, Bartosz LU (2018) In Journal of Functional Analysis
Abstract

We consider Hilbert spaces of analytic functions in the disk with a normalized reproducing kernel and such that the backward shift f(z)↦[Formula presented] is a contraction on the space. We present a model for this operator and use it to prove the surprising result that functions which extend continuously to the closure of the disk are dense in the space. This has several applications, for example we can answer a question regarding reverse Carleson embeddings for these spaces. We also identify a large class of spaces which are similar to the de Branges–Rovnyak spaces and prove some results which are new even in the classical case.

Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
epub
subject
keywords
Backward shift, Hilbert spaces of analytic functions
in
Journal of Functional Analysis
publisher
Elsevier
external identifiers
  • scopus:85052333770
ISSN
0022-1236
DOI
10.1016/j.jfa.2018.08.019
language
English
LU publication?
yes
id
8497ce4b-adc0-4c87-8933-5dcbf98d6c46
date added to LUP
2018-09-28 07:34:44
date last changed
2019-02-20 11:28:12
@article{8497ce4b-adc0-4c87-8933-5dcbf98d6c46,
  abstract     = {<p>We consider Hilbert spaces of analytic functions in the disk with a normalized reproducing kernel and such that the backward shift f(z)↦[Formula presented] is a contraction on the space. We present a model for this operator and use it to prove the surprising result that functions which extend continuously to the closure of the disk are dense in the space. This has several applications, for example we can answer a question regarding reverse Carleson embeddings for these spaces. We also identify a large class of spaces which are similar to the de Branges–Rovnyak spaces and prove some results which are new even in the classical case.</p>},
  author       = {Aleman, Alexandru and Malman, Bartosz},
  issn         = {0022-1236},
  keyword      = {Backward shift,Hilbert spaces of analytic functions},
  language     = {eng},
  month        = {08},
  publisher    = {Elsevier},
  series       = {Journal of Functional Analysis},
  title        = {Hilbert spaces of analytic functions with a contractive backward shift},
  url          = {http://dx.doi.org/10.1016/j.jfa.2018.08.019},
  year         = {2018},
}