Extensions of symmetric operators I: The inner characteristic function case

R.T.W. Martin

Concrete Operators (2015)

  • Volume: 2, Issue: 1, page 53-97, electronic only
  • ISSN: 2299-3282

Abstract

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Given a symmetric linear transformation on a Hilbert space, a natural problem to consider is the characterization of its set of symmetric extensions. This problem is equivalent to the study of the partial isometric extensions of a fixed partial isometry. We provide a new function theoretic characterization of the set of all self-adjoint extensions of any symmetric linear transformation B with finite equal indices and inner Livšic characteristic function θB by constructing a bijection between the quotient of this set by a certain natural equivalence relation and the set of all contractive analytic functions φ which are greater or equal to θB.

How to cite

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R.T.W. Martin. "Extensions of symmetric operators I: The inner characteristic function case." Concrete Operators 2.1 (2015): 53-97, electronic only. <http://eudml.org/doc/271058>.

@article{R2015,
abstract = {Given a symmetric linear transformation on a Hilbert space, a natural problem to consider is the characterization of its set of symmetric extensions. This problem is equivalent to the study of the partial isometric extensions of a fixed partial isometry. We provide a new function theoretic characterization of the set of all self-adjoint extensions of any symmetric linear transformation B with finite equal indices and inner Livšic characteristic function θB by constructing a bijection between the quotient of this set by a certain natural equivalence relation and the set of all contractive analytic functions φ which are greater or equal to θB.},
author = {R.T.W. Martin},
journal = {Concrete Operators},
keywords = {symmetric operators; partial isometries; self-adjoint and unitary extensions; reproducing kernel Hilbert spaces of analytic functions; Hardy and deBranges Rovnyak spaces; Livšic characteristic function; self-adjoint extensions; unitary extensions; reproducing kernel; Hilbert spaces of analytic functions; Hardy spaces; Debranges Rovnyak spaces; Livšic characteristic function; inner fuctions},
language = {eng},
number = {1},
pages = {53-97, electronic only},
title = {Extensions of symmetric operators I: The inner characteristic function case},
url = {http://eudml.org/doc/271058},
volume = {2},
year = {2015},
}

TY - JOUR
AU - R.T.W. Martin
TI - Extensions of symmetric operators I: The inner characteristic function case
JO - Concrete Operators
PY - 2015
VL - 2
IS - 1
SP - 53
EP - 97, electronic only
AB - Given a symmetric linear transformation on a Hilbert space, a natural problem to consider is the characterization of its set of symmetric extensions. This problem is equivalent to the study of the partial isometric extensions of a fixed partial isometry. We provide a new function theoretic characterization of the set of all self-adjoint extensions of any symmetric linear transformation B with finite equal indices and inner Livšic characteristic function θB by constructing a bijection between the quotient of this set by a certain natural equivalence relation and the set of all contractive analytic functions φ which are greater or equal to θB.
LA - eng
KW - symmetric operators; partial isometries; self-adjoint and unitary extensions; reproducing kernel Hilbert spaces of analytic functions; Hardy and deBranges Rovnyak spaces; Livšic characteristic function; self-adjoint extensions; unitary extensions; reproducing kernel; Hilbert spaces of analytic functions; Hardy spaces; Debranges Rovnyak spaces; Livšic characteristic function; inner fuctions
UR - http://eudml.org/doc/271058
ER -

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