H-n-perturbations of self-adjoint operators and Krein's resolvent formula
(2003) In Integral Equations and Operator Theory 45(4). p.437-460- Abstract
- Supersingular H-n rank one perturbations of an arbitrary positive self-adjoint operator A acting in the Hilbert space H are investigated. The operator corresponding to the formal expression A(alpha) = A + alpha(phi,.)phi, alpha is an element of R, phi is an element of H-n (A), is determined as a regular operator with pure real spectrum acting in a certain extended Hilbert space H superset of X The resolvent of the operator so defined is given by a certain generalization of Krein's resolvent formula. It is proven that the spectral properties of the operator are described by generalized Nevanlinna functions. The results of [24] are extended to the case of arbitrary integer n greater than or equal to 4.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/312758
- author
- Kurasov, Pavel LU
- organization
- publishing date
- 2003
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- singular perturbations, Krein's formula, Nevanlinna functions
- in
- Integral Equations and Operator Theory
- volume
- 45
- issue
- 4
- pages
- 437 - 460
- publisher
- Springer
- external identifiers
-
- wos:000182448500004
- scopus:0037275339
- ISSN
- 1420-8989
- DOI
- 10.1007/s000200300015
- language
- English
- LU publication?
- yes
- id
- eaf71e87-b0ca-4d4e-a569-6dfa4f76dcf5 (old id 312758)
- date added to LUP
- 2016-04-01 16:24:27
- date last changed
- 2022-03-07 05:43:38
@article{eaf71e87-b0ca-4d4e-a569-6dfa4f76dcf5, abstract = {{Supersingular H-n rank one perturbations of an arbitrary positive self-adjoint operator A acting in the Hilbert space H are investigated. The operator corresponding to the formal expression A(alpha) = A + alpha(phi,.)phi, alpha is an element of R, phi is an element of H-n (A), is determined as a regular operator with pure real spectrum acting in a certain extended Hilbert space H superset of X The resolvent of the operator so defined is given by a certain generalization of Krein's resolvent formula. It is proven that the spectral properties of the operator are described by generalized Nevanlinna functions. The results of [24] are extended to the case of arbitrary integer n greater than or equal to 4.}}, author = {{Kurasov, Pavel}}, issn = {{1420-8989}}, keywords = {{singular perturbations; Krein's formula; Nevanlinna functions}}, language = {{eng}}, number = {{4}}, pages = {{437--460}}, publisher = {{Springer}}, series = {{Integral Equations and Operator Theory}}, title = {{H-n-perturbations of self-adjoint operators and Krein's resolvent formula}}, url = {{http://dx.doi.org/10.1007/s000200300015}}, doi = {{10.1007/s000200300015}}, volume = {{45}}, year = {{2003}}, }