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

Pavel Kurasov

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
Pages (from-to)437-460
JournalIntegral Equations and Operator Theory
Volume45
Issue number4
DOIs
Publication statusPublished - 2003

Subject classification (UKÄ)

  • Mathematics

Free keywords

  • singular perturbations
  • Krein's formula
  • Nevanlinna functions

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