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On supersingular perturbations of non-semibounded self-adjoint operators
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 32019 (English)In: Journal of operator theory, ISSN 0379-4024, E-ISSN 1841-7744, Vol. 81, no 1, p. 195-223Article in journal (Refereed) Published
Abstract [en]

In this paper self-adjoint realizations of the formal expression A(alpha ):= A + alpha <phi, .> phi are described, where alpha is an element of R boolean OR {infinity}, the operator A is self-adjoint in a Hilbert space H and phi is a supersingular element from the scale space H--(n) (-2) (A) \H--(n) (-1) (A) for n >= 1. The crucial point is that the spectrum of A may consist of the whole real line. We construct two models to describe the family (A(alpha)). It can be interpreted in a Hilbert space with a twisted version of Krein's formula, or with a more classical version of Krein's formula but in a Pontryagin space. Finally, we compare the two approaches in terms of the respective Q-functions.

Place, publisher, year, edition, pages
2019. Vol. 81, no 1, p. 195-223
Keywords [en]
Unbounded self-adjoint operator, supersingular perturbation, generalized Nevanlinna function
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-166640DOI: 10.7900/jot.2017dec22.2183ISI: 000458790000009OAI: oai:DiVA.org:su-166640DiVA, id: diva2:1296375
Available from: 2019-03-15 Created: 2019-03-15 Last updated: 2019-03-15Bibliographically approved

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