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On J-self-adjoint operators with stable C-symmetries

Published online by Cambridge University Press:  30 January 2013

Seppo Hassi  and
Sergii Kuzhel
Seppo Hassi
Affiliation:
Department of Mathematics and Statistics, University of Vaasa, 65101 Vaasa, Finland ([email protected])
Sergii Kuzhel
Affiliation:
AGH University of Science and Technology, 30-059 Krakow, Poland ([email protected])
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Abstract

The paper is devoted to the development of the theory of self-adjoint operators in Krein spaces (J-self-adjoint operators) involving some additional properties arising from the existence of C-symmetries. We mainly focus on the recent notion of stable C-symmetry for J-self-adjoint extensions of a symmetric operator S. The general results involve boundary value techniques and reproducing kernel space methods, and they include an explicit functional model for the class of stable C-symmetries. Some of the results are specialized further by studying the case where S has defect numbers 〈2,2〉 in detail.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 143 , Issue 1 , February 2013 , pp. 141 - 167
Copyright
Copyright © Royal Society of Edinburgh 2013

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