NDLI: Unitary Perturbations of Compressed n-Dimensional Shifts

Content Provider	Springer Nature Link
Author	Martin, R. T. W.
Copyright Year	2012
Abstract	Given any contractive matrix-valued analytic function $${\Theta}$$ on the unit disc $${\mathbb{D}}$$ , we construct a $${\mathcal{U}(n)}$$ -parameter family of unitary operators which correspond to $${\Theta}$$ in a natural way. These operators are unitarily equivalent to higher dimensional analogues of Clark’s unitary perturbations, a family of unitary operators associated to any self-map of the unit disc. Clark’s unitary perturbations were introduced in a seminal paper of Clark which has inspired the study of what are now called Aleksandrov–Clark measures. Our higher dimensional analogues of Clark’s unitary perturbations are applied to obtain matrix-generalizations of several classical results on the Aleksandrov–Clark measures associated to any holomorphic self-map of the unit disc. In particular we establish a matrix-valued Aleksandrov disintegration theorem for the Aleksandrov–Clark measures associated with matrix-valued contractive analytic functions $${\Theta}$$ , and, by following results of Clark and Fricain in the scalar case, we provide a necessary and sufficient condition for the de Branges–Rovnyak space associated with $${\Theta}$$ to contain a total orthogonal set of point evaluation vectors.
Starting Page	765
Ending Page	799
Page Count	35
File Format	PDF
ISSN	16618254
Journal	Complex Analysis and Operator Theory
Volume Number	7
Issue Number	4
e-ISSN	16618262
Language	English
Publisher	Springer Basel
Publisher Date	2012-09-30
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Hardy space Model subspaces Aleksandrov disintegration theorem Clark’s unitary perturbations Aleksandrov–Clark measures Matrix-analytic functions Symmetric/isometric linear transformations Hardy spaces Bounded analytic functions Operators in reproducing-kernel Hilbert spaces Operators on function spaces Hilbert spaces with reproducing kernels Summability and bases Banach algebras of differentiable or analytic functions, $H^p$-spaces Symmetric and selfadjoint operators Mathematics Operator Theory Analysis
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Theory and Mathematics Computational 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

Reproducing Kernels and Radial Differential Operators for Holomorphic and Harmonic Besov Spaces on Unit Balls: a Unified View

An Invariant Subspace Theorem and Invariant Subspaces of Analytic Reproducing Kernel Hilbert Spaces - II

Symmetric Operators and Reproducing Kernel Hilbert Spaces

Representation of Simple Symmetric Operators with Deficiency Indices (1, 1) in de Branges Space

Triplets of Closely Embedded Dirichlet Type Spaces on the Unit Polydisc

Boundary Behavior of Functions in the de Branges–Rovnyak Spaces

Aleksandrov-Clark theory for the Drury-Arveson space

Hardy-Type Spaces Arising from a Vector-Valued Cauchy Kernel

Factorizations of Kernels and Reproducing Kernel Hilbert Spaces

Unitary Perturbations of Compressed n-Dimensional Shifts

Similar Documents

Reproducing Kernels and Radial Differential Operators for Holomorphic and Harmonic Besov Spaces on Unit Balls: a Unified View

An Invariant Subspace Theorem and Invariant Subspaces of Analytic Reproducing Kernel Hilbert Spaces - II

Symmetric Operators and Reproducing Kernel Hilbert Spaces

Representation of Simple Symmetric Operators with Deficiency Indices (1, 1) in de Branges Space

Triplets of Closely Embedded Dirichlet Type Spaces on the Unit Polydisc

Boundary Behavior of Functions in the de Branges–Rovnyak Spaces

Aleksandrov-Clark theory for the Drury-Arveson space

Hardy-Type Spaces Arising from a Vector-Valued Cauchy Kernel

Factorizations of Kernels and Reproducing Kernel Hilbert Spaces

Unitary Perturbations of Compressed n-Dimensional Shifts