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H-n-perturbations of self-adjoint operators and Krein's resolvent formula

Kurasov, Pavel LU (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:
author
organization
publishing date
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
2007-09-16 10:55:19
date last changed
2018-10-03 11:43:18
@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},
  keyword      = {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},
  volume       = {45},
  year         = {2003},
}