NDLI: Some remarks on analytic continuation in weighted backward shift invariant subspaces

Content Provider	Springer Nature Link
Author	Hartmann, Andreas
Copyright Year	2010
Abstract	By a famous result of Douglas, Shapiro, and Shields, functions in backward shift invariant subspaces in Hardy spaces are characterized by the fact that they admit a pseudocontinuation outside the closed unit disk. More can be said when the spectrum of the associated inner function has holes on $${{\mathbb T}}$$ . Then the functions of the invariant subspaces even extend analytically through these holes. Here we will be interested in weighted backward shift invariant subspaces which appear naturally in the context of kernels of Toeplitz operators. Note that such kernels are special cases of so-called nearly invariant subspaces. In our setting a result by Aleksandrov allows to deduce analytic continuation properties which we will then apply to consider embeddings of weighted invariant subspaces into their unweighted companions. We hope that this connection might shed some new light on known results. We will also establish a link between the spectrum of the inner function and the approximate point spectrum of the backward shift in the weighted situation in the spirit of results by Aleman, Richter, and Ross.
Ending Page	75
Page Count	17
Starting Page	59
File Format	PDF
ISSN	0003889X
e-ISSN	14208938
Journal	Archiv der Mathematik
Issue Number	1
Volume Number	96
Language	English
Publisher	SP Birkhäuser Verlag Basel
Publisher Date	2010-12-07
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Backward shift Rigid function Invariant subspaces Invariant subspace Analytic continuation Embedding Operators on special spaces (weighted shifts, operators on sequence spaces, etc.) Mathematics Muckenhoupt condition Toeplitz operators Spectrum
Content Type	Text
Resource Type	Article
Subject	Mathematics

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Regularity on the boundary in spaces of holomorphic functions on the unit disk

Regularity on the boundary in spaces of holomorphic functions on the unit disk

Failure of the wandering subspace property for analytic norm-increasing $3$-isometries

Rank-one cross commutators on backward shift invariant subspaces on the bidisk

Mixed invariant subspaces over the bidisk II

Invariant subspaces for Bishop operators and beyond

Reducing Subspaces on the Annulus

Mixed Invariant Subspaces over the Bidisk

The invariant subspaces of $ S\oplus S^* $

Some remarks on analytic continuation in weighted backward shift invariant subspaces

Similar Documents

Regularity on the boundary in spaces of holomorphic functions on the unit disk

Regularity on the boundary in spaces of holomorphic functions on the unit disk

Failure of the wandering subspace property for analytic norm-increasing $3$-isometries

Rank-one cross commutators on backward shift invariant subspaces on the bidisk

Mixed invariant subspaces over the bidisk II

Invariant subspaces for Bishop operators and beyond

Reducing Subspaces on the Annulus

Mixed Invariant Subspaces over the Bidisk

The invariant subspaces of $ S\oplus S^* $

Some remarks on analytic continuation in weighted backward shift invariant subspaces