# Extensions of symmetric operators I: The inner characteristic function case

Concrete Operators (2015)

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

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topR.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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