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.
@article{bwmeta1.element.doi-10_1515_conop-2015-0004,
author = {R.T.W. Martin},
title = {Extensions of symmetric operators I: The inner characteristic function case},
journal = {Concrete Operators},
volume = {2},
year = {2015},
zbl = {06477134},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_conop-2015-0004}
}
R.T.W. Martin. Extensions of symmetric operators I: The inner characteristic function case. Concrete Operators, Tome 2 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_conop-2015-0004/
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