NDLI: Boundary Relations, Unitary Colligations, and Functional Models

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Complex Analysis and Operator Theory : Volume 11

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Complex Analysis and Operator Theory : Volume 7

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Complex Analysis and Operator Theory : Volume 5

Complex Analysis and Operator Theory : Volume 4

Complex Analysis and Operator Theory : Volume 3

Complex Analysis and Operator Theory : Volume 3, Issue 4, December 2009

Complex Analysis and Operator Theory : Volume 3, Issue 3, October 2009

Complex Analysis and Operator Theory : Volume 3, Issue 2, May 2009

Complex Analysis and Operator Theory : Volume 3, Issue 1, March 2009

Radial Multiresolution, Cuntz Algebras Representations and an Application to Fractals

Passive Systems with a Normal Main Operator and Quasi-selfadjoint Systems

Boundary Relations, Unitary Colligations, and Functional Models

Borel–Carathéodory Type Theorem for Monogenic Functions

Boundedness of Convolution Operators and Input–Output Maps between Weighted Spaces

On H. Weyl and J. Steiner Polynomials

The Poisson Kernel for Hardy Algebras

Operator Valued Functions with Pick Operators Having Negative Subspaces of Bounded Dimensions

Weyl–Titchmarsh Function of an Abstract Boundary Value Problem, Operator Colligations, and Linear Systems with Boundary Control

Stable Ranks of Banach Algebras of Operator-Valued Analytic Functions

Complex Analysis and Operator Theory : Volume 2

Complex Analysis and Operator Theory : Volume 1

Boundary Relations, Unitary Colligations, and Functional Models

Content Provider	Springer Nature Link
Author	Behrndt, Jussi Hassi, Seppo So, Henk
Copyright Year	2008
Abstract	Recently a new notion, the so-called boundary relation, has been introduced involving an analytic object, the so-called Weyl family. Weyl families and boundary relations establish a link between the class of Nevanlinna families and unitary relations acting from one Kreĭn space, a basic (state) space, to another Kreĭn space, a parameter space where the Nevanlinna family or Weyl family is acting. Nevanlinna families are a natural generalization of the class of operator-valued Nevanlinna functions and they are closely connected with the class of operator-valued Schur functions. This paper establishes the connection between boundary relations and their Weyl families on the one hand, and unitary colligations and their transfer functions on the other hand. From this connection there are various advances which will benefit the investigations on both sides, including operator theoretic as well as analytic aspects. As one of the main consequences a functional model for Nevanlinna families is obtained from a variant of the functional model of L. de Branges and J. Rovnyak for Schur functions. Here the model space is a reproducing kernel Hilbert space in which multiplication by the independent variable defines a closed simple symmetric operator. This operator gives rise to a boundary relation such that the given Nevanlinna family is realized as the corresponding Weyl family.
Starting Page	57
Ending Page	98
Page Count	42
File Format	PDF
ISSN	16618254
Journal	Complex Analysis and Operator Theory
Volume Number	3
Issue Number	1
e-ISSN	16618262
Language	English
Publisher	Birkhäuser-Verlag
Publisher Date	2008-05-19
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Boundary relation boundary triplet Weyl family Weyl function Nevanlinna family Nevanlinna function unitary colligation transfer function Schur function reproducing kernel Hilbert space functional model Hilbert spaces with reproducing kernels Operators in reproducing-kernel Hilbert spaces Linear relations Symmetric and selfadjoint operators Mathematics Operator Theory Analysis
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Theory and Mathematics Computational Mathematics

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Boundary relations, unitary colligations, and functional models (2009).

Symmetric Operators and Reproducing Kernel Hilbert Spaces

Functional models for Nevanlinna families

Test Functions, Schur–Agler Classes and Transfer-Function Realizations: The Matrix-Valued Setting

Functional models for Nevanlinna families

Scattering Systems with Several Evolutions and Formal 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

Unitary Equivalence of Proper Extensions of a Symmetric Operator and the Weyl Function

Boundary Relations, Unitary Colligations, and Functional Models

Similar Documents

Boundary relations, unitary colligations, and functional models (2009).

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Functional models for Nevanlinna families

Test Functions, Schur–Agler Classes and Transfer-Function Realizations: The Matrix-Valued Setting

Functional models for Nevanlinna families

Scattering Systems with Several Evolutions and Formal Reproducing Kernel Hilbert Spaces

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