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Backward Shift and Nearly Invariant Subspaces of Fock-type Spaces

Aleman, Alexandru LU ; Baranov, Anton ; Belov, Yurii and Hedenmalm, Haakan (2022) In International Mathematics Research Notices 2022(10). p.7390-7419
Abstract

We study the structure of the backward shift invariant and nearly invariant subspaces in weighted Fock-type spaces ℱWp, whose weight is not necessarily radial. We show that in the spaces ℱWp, which contain the polynomials as a dense subspace (in particular, in the radial case), all nontrivial backward shift invariant subspaces are of the form ℘n, that is, finite-dimensional subspaces consisting of polynomials of degree at most n. In general, the structure of the nearly invariant subspaces is more complicated. In the case of spaces of slow growth (up to zero exponential type), we establish an analogue of de Branges' ordering theorem. We then construct examples that show that the result fails for general Fock-type spaces of larger growth.... (More)

We study the structure of the backward shift invariant and nearly invariant subspaces in weighted Fock-type spaces ℱWp, whose weight is not necessarily radial. We show that in the spaces ℱWp, which contain the polynomials as a dense subspace (in particular, in the radial case), all nontrivial backward shift invariant subspaces are of the form ℘n, that is, finite-dimensional subspaces consisting of polynomials of degree at most n. In general, the structure of the nearly invariant subspaces is more complicated. In the case of spaces of slow growth (up to zero exponential type), we establish an analogue of de Branges' ordering theorem. We then construct examples that show that the result fails for general Fock-type spaces of larger growth.

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author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
International Mathematics Research Notices
volume
2022
issue
10
pages
30 pages
publisher
Oxford University Press
external identifiers
  • scopus:85132881482
ISSN
1073-7928
DOI
10.1093/imrn/rnaa338
language
English
LU publication?
yes
id
858ddc4b-f11d-479f-92d8-daa7037dce46
date added to LUP
2022-09-06 12:55:45
date last changed
2022-09-06 12:55:45
@article{858ddc4b-f11d-479f-92d8-daa7037dce46,
  abstract     = {{<p>We study the structure of the backward shift invariant and nearly invariant subspaces in weighted Fock-type spaces ℱWp, whose weight is not necessarily radial. We show that in the spaces ℱWp, which contain the polynomials as a dense subspace (in particular, in the radial case), all nontrivial backward shift invariant subspaces are of the form ℘n, that is, finite-dimensional subspaces consisting of polynomials of degree at most n. In general, the structure of the nearly invariant subspaces is more complicated. In the case of spaces of slow growth (up to zero exponential type), we establish an analogue of de Branges' ordering theorem. We then construct examples that show that the result fails for general Fock-type spaces of larger growth. </p>}},
  author       = {{Aleman, Alexandru and Baranov, Anton and Belov, Yurii and Hedenmalm, Haakan}},
  issn         = {{1073-7928}},
  language     = {{eng}},
  month        = {{05}},
  number       = {{10}},
  pages        = {{7390--7419}},
  publisher    = {{Oxford University Press}},
  series       = {{International Mathematics Research Notices}},
  title        = {{Backward Shift and Nearly Invariant Subspaces of Fock-type Spaces}},
  url          = {{http://dx.doi.org/10.1093/imrn/rnaa338}},
  doi          = {{10.1093/imrn/rnaa338}},
  volume       = {{2022}},
  year         = {{2022}},
}