Publications [#330334] of Alexander A. Kiselev

Papers Published

1. Kiselev, A; Simon, B, Rank one perturbations with infinitesimal coupling, Journal of Functional Analysis, vol. 130 no. 2 (January, 1995), pp. 345-356, Elsevier BV [doi]
   (last updated on 2026/01/16)

   Abstract:
   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.