High order singular rank one perturbations of a positive operator

A Dijksma, Pavel Kurasov, Y Shondin

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)209-245
JournalIntegral Equations and Operator Theory
Volume53
Issue number2
DOIs
Publication statusPublished - 2005

Subject classification (UKÄ)

  • Mathematics

Keywords

  • self-adjoint extension
  • symmetric operator
  • Q-function
  • function
  • defect
  • Pontryagin space
  • Hilbert space
  • scale of Hilbert spaces
  • rank
  • one perturbation
  • Gelfand triple

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