Backward Shift and Nearly Invariant Subspaces of Fock-type Spaces

Standard

Backward Shift and Nearly Invariant Subspaces of Fock-type Spaces. / Aleman, Alexandru; Baranov, Anton ; Belov, Yurii ; Hedenmalm, Haakan.

In: International Mathematics Research Notices, Vol. 2022, No. 10, 10.05.2022, p. 7390-7419.

Research output: Contribution to journal › Article › peer-review

Author

Aleman, Alexandru ; Baranov, Anton ; Belov, Yurii ; Hedenmalm, Haakan. / Backward Shift and Nearly Invariant Subspaces of Fock-type Spaces. In: International Mathematics Research Notices. 2022 ; Vol. 2022, No. 10. pp. 7390-7419.

BibTeX

@article{910fc76b3b854a8184cc6915080c1e2f,

title = "Backward Shift and Nearly Invariant Subspaces of Fock-type Spaces",

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. ",

author = "Alexandru Aleman and Anton Baranov and Yurii Belov and Haakan Hedenmalm",

note = "Publisher Copyright: {\textcopyright} 2021 The Author(s).",

year = "2022",

month = may,

day = "10",

doi = "10.1093/imrn/rnaa338",

language = "English",

volume = "2022",

pages = "7390--7419",

journal = "International Mathematics Research Notices",

issn = "1073-7928",

publisher = "Oxford University Press",

number = "10",

}

RIS

TY - JOUR

T1 - Backward Shift and Nearly Invariant Subspaces of Fock-type Spaces

AU - Aleman, Alexandru

AU - Baranov, Anton

AU - Belov, Yurii

AU - Hedenmalm, Haakan

PY - 2022/5/10

Y1 - 2022/5/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85132881482&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/30bbf92d-6e3a-38cd-ac20-aa0859a82c9f/

U2 - 10.1093/imrn/rnaa338

DO - 10.1093/imrn/rnaa338

M3 - Article

AN - SCOPUS:85132881482

VL - 2022

SP - 7390

EP - 7419

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 10

ER -

ID: 97909696