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High order singular rank one perturbations of a positive operator

Dijksma, A ; Kurasov, Pavel LU and Shondin, Y (2005) In Integral Equations and Operator Theory 53(2). p.209-245
Abstract
In this paper self-adjoint realizations in Hilbert and Pontryagin spaces of the formal expression L-alpha = L + <(.),psi >psi are discussed and compared. Here L is a positive self-adjoint operator in a Hilbert space H with inner product <(.), (.)>, a is a real parameter, and p in the rank one perturbation is a singular element belonging to H-nH-n+1 with n >= 3, where {H-s}(s=-infinity)(infinity) is the scale of Hilbert spaces associated with L in H.
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author
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organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
self-adjoint extension, symmetric operator, Q-function, function, defect, Pontryagin space, Hilbert space, scale of Hilbert spaces, rank, one perturbation, Gelfand triple
in
Integral Equations and Operator Theory
volume
53
issue
2
pages
209 - 245
publisher
Springer
external identifiers
  • wos:000233027600003
  • scopus:25644438431
ISSN
1420-8989
DOI
10.1007/s00020-005-1357-5
language
English
LU publication?
yes
id
78c1ce0a-a96b-4adb-8706-ceb0290c91cd (old id 214232)
date added to LUP
2016-04-01 16:08:32
date last changed
2025-10-14 09:13:01
@article{78c1ce0a-a96b-4adb-8706-ceb0290c91cd,
  abstract     = {{In this paper self-adjoint realizations in Hilbert and Pontryagin spaces of the formal expression L-alpha = L + &lt;(.),psi &gt;psi are discussed and compared. Here L is a positive self-adjoint operator in a Hilbert space H with inner product &lt;(.), (.)&gt;, a is a real parameter, and p in the rank one perturbation is a singular element belonging to H-nH-n+1 with n &gt;= 3, where {H-s}(s=-infinity)(infinity) is the scale of Hilbert spaces associated with L in H.}},
  author       = {{Dijksma, A and Kurasov, Pavel and Shondin, Y}},
  issn         = {{1420-8989}},
  keywords     = {{self-adjoint extension; symmetric operator; Q-function; function; defect; Pontryagin space; Hilbert space; scale of Hilbert spaces; rank; one perturbation; Gelfand triple}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{209--245}},
  publisher    = {{Springer}},
  series       = {{Integral Equations and Operator Theory}},
  title        = {{High order singular rank one perturbations of a positive operator}},
  url          = {{http://dx.doi.org/10.1007/s00020-005-1357-5}},
  doi          = {{10.1007/s00020-005-1357-5}},
  volume       = {{53}},
  year         = {{2005}},
}