Backward Shift and Nearly Invariant Subspaces of Fock-type Spaces

Aleman, AlexandruLund University,Lunds universitet,Matematik (naturvetenskapliga fakulteten),Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematics (Faculty of Sciences),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH (author)

QC 20230327
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.

Baranov, A.Saint Petersburg State University (author)
Belov, Y.Saint Petersburg State University (author)
Hedenmalm, Håkan,1961-KTH Royal Institute of Technology,KTH,Matematik (Avd.)(Swepub:kth)u1nfrlkz (author)
Matematik (naturvetenskapliga fakulteten)Matematikcentrum (creator_code:org_t)

In:International mathematics research notices: Oxford University Press (OUP)2022:10, s. 7390-74191073-79281687-0247

By the author/editor: Aleman, Alexandr ...; Baranov, A.; Belov, Y.; Hedenmalm, Håkan ...

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NATURAL SCIENCES: NATURAL SCIENCES; and Mathematics; and Mathematical Ana ...

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