High order singular rank one perturbations of a positive operator
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/214232
- author
- Dijksma, A ; Kurasov, Pavel LU and Shondin, Y
- organization
- publishing date
- 2005
- 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
- 2022-03-30 05:48:52
@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 + <(.),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.}}, 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}}, }