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Concrete Operators

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Mathematical Citation Quotient (MCQ) 2016: 0.38


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Extensions of symmetric operators I: The inner characteristic function case

R.T.W. Martin
Published Online: 2015-07-10 | DOI: https://doi.org/10.1515/conop-2015-0004

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.

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

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About the article

Received: 2015-04-01

Accepted: 2015-06-16

Published Online: 2015-07-10


Citation Information: Concrete Operators, ISSN (Online) 2299-3282, DOI: https://doi.org/10.1515/conop-2015-0004.

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© 2015 R.T.W. Martin. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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