Generalized Schur functions and related de Branges-Rovnyak spaces in the banach space setting

Daniel Alpay; Olga Timoshenko; Prasad Vegulla; Dan Volok

doi:10.1007/s00020-009-1723-9

Generalized Schur functions and related de Branges-Rovnyak spaces in the banach space setting

Daniel Alpay, Olga Timoshenko, Prasad Vegulla, Dan Volok

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We study the analogues of de Branges-Rovnyak spaces in the Banach space case. An important role is played by self-adjoint operators from the dual of a Banach space into the Banach space itself. A factorization theorem for such operators is proved in the case when they have a finite number of negative squares.

Original language	English
Pages (from-to)	449-472
Number of pages	24
Journal	Integral Equations and Operator Theory
Volume	65
Issue number	4
DOIs	https://doi.org/10.1007/s00020-009-1723-9
State	Published - 1 Dec 2009

Keywords

De Branges-Rovnyak spaces
Positive operators
Realization theory
Reproducing kernel Pontryagin space
Schur functions

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.1007/s00020-009-1723-9

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title = "Generalized Schur functions and related de Branges-Rovnyak spaces in the banach space setting",

abstract = "We study the analogues of de Branges-Rovnyak spaces in the Banach space case. An important role is played by self-adjoint operators from the dual of a Banach space into the Banach space itself. A factorization theorem for such operators is proved in the case when they have a finite number of negative squares.",

keywords = "De Branges-Rovnyak spaces, Positive operators, Realization theory, Reproducing kernel Pontryagin space, Schur functions",

author = "Daniel Alpay and Olga Timoshenko and Prasad Vegulla and Dan Volok",

note = "Funding Information: D. Alpay thanks the Earl Katz family for endowing the chair which supported his research. This research is part of the European Science Foundation Networking Program HCAA, and was supported in part by the Israel Science Foundation grant 1023/07.",

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doi = "10.1007/s00020-009-1723-9",

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AU - Alpay, Daniel

AU - Timoshenko, Olga

AU - Vegulla, Prasad

AU - Volok, Dan

N1 - Funding Information: D. Alpay thanks the Earl Katz family for endowing the chair which supported his research. This research is part of the European Science Foundation Networking Program HCAA, and was supported in part by the Israel Science Foundation grant 1023/07.

PY - 2009/12/1

Y1 - 2009/12/1

N2 - We study the analogues of de Branges-Rovnyak spaces in the Banach space case. An important role is played by self-adjoint operators from the dual of a Banach space into the Banach space itself. A factorization theorem for such operators is proved in the case when they have a finite number of negative squares.

AB - We study the analogues of de Branges-Rovnyak spaces in the Banach space case. An important role is played by self-adjoint operators from the dual of a Banach space into the Banach space itself. A factorization theorem for such operators is proved in the case when they have a finite number of negative squares.

KW - De Branges-Rovnyak spaces

KW - Positive operators

KW - Realization theory

KW - Reproducing kernel Pontryagin space

KW - Schur functions

UR - http://www.scopus.com/inward/record.url?scp=76449087301&partnerID=8YFLogxK

U2 - 10.1007/s00020-009-1723-9

DO - 10.1007/s00020-009-1723-9

M3 - Article

AN - SCOPUS:76449087301

SN - 0378-620X

VL - 65

SP - 449

EP - 472

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 4

ER -

Generalized Schur functions and related de Branges-Rovnyak spaces in the banach space setting

Abstract

Keywords

ASJC Scopus subject areas

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