Hnperturbations of selfadjoint operators and Krein's resolvent formula
(2003) In Integral Equations and Operator Theory 45(4). p.437460 Abstract
 Supersingular Hn rank one perturbations of an arbitrary positive selfadjoint 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 Hn (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
 14208989
 DOI
 10.1007/s000200300015
 language
 English
 LU publication?
 yes
 id
 eaf71e87b0ca4d4ea5696dfa4f76dcf5 (old id 312758)
 date added to LUP
 20160401 16:24:27
 date last changed
 20210427 01:26:59
@article{eaf71e87b0ca4d4ea5696dfa4f76dcf5, abstract = {Supersingular Hn rank one perturbations of an arbitrary positive selfadjoint 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 Hn (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 = {14208989}, language = {eng}, number = {4}, pages = {437460}, publisher = {Springer}, series = {Integral Equations and Operator Theory}, title = {Hnperturbations of selfadjoint operators and Krein's resolvent formula}, url = {http://dx.doi.org/10.1007/s000200300015}, doi = {10.1007/s000200300015}, volume = {45}, year = {2003}, }