Infinite-dimensional perturbations, maximally nondensely defined symmetric operators, and some matrix representations

Hassi, Seppo; de Snoo, H.S.V.; Szafraniec, F.H. (2012-12)
 
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https://doi.org/10.1016/j.indag.2012.08.007

Hassi, Seppo
de Snoo, H.S.V.
Szafraniec, F.H.
Elsevier Royal Netherlands Academy of Arts and Sciences (KNAW)
12 / 2012
doi:10.1016/j.indag.2012.08.007
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http://urn.fi/URN:NBN:fi-fe2020102185819

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©2012 Elsevier. This manuscript version is made available under the Creative Commons Attribution–NonCommercial–NoDerivatives 4.0 International (CC BY–NC–ND 4.0) license, https://creativecommons.org/licenses/by-nc-nd/4.0/
Tiivistelmä
The notion of a maximally nondensely defined symmetric operator or relation is introduced and characterized. The selfadjoint extensions (including the generalized Friedrichs extension) of a class of maximally nondensely defined symmetric operators are described. The description is given by means of the theory of ordinary boundary triplets and exhibits the extensions as infinite-dimensional perturbations of a certain selfadjoint operator extension of the symmetric operator.
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