Backward Shift and Nearly Invariant Subspaces of Fock-type Spaces

Alexandru Aleman, Anton Baranov, Yurii Belov, Haakan Hedenmalm

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)7390-7419
Number of pages30
JournalInternational Mathematics Research Notices
Issue number10
Publication statusPublished - 2022 May 1

Subject classification (UKÄ)

  • Mathematical Analysis


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