Rank one perturbations with infinitesimal coupling

Journal Article (Journal Article)

We consider a positive self-adjoint operator A and formal rank one perturbations B = A + α(φ, ·)φ, where φ ∈ H-2(A) but φ ∉ H-1 (A), with Hs(A) the usual scale of spaces. We show that B can be defined for such φ and what are essentially negative infinitesimal values of α. In a sense we will make precise, every rank one perturbation is one of three forms: (i) φ ∈ H-1(A), α ∈ R; (ii) φ ∈ H-1, α = ∞; or (iii) the new type we consider here. © 1995 Academic Press Limited.

Full Text

Duke Authors

Cited Authors

  • Kiselev, A; Simon, B

Published Date

  • January 1, 1995

Published In

Volume / Issue

  • 130 / 2

Start / End Page

  • 345 - 356

Electronic International Standard Serial Number (EISSN)

  • 1096-0783

International Standard Serial Number (ISSN)

  • 0022-1236

Digital Object Identifier (DOI)

  • 10.1006/jfan.1995.1074

Citation Source

  • Scopus