On the similarity of some differential operators to self-adjoint ones

Academic Article

Abstract

  • The paper is devoted to the study of the similarity to self-adjoint operators of operators of the form L = - sign x/|x| αp(x) d 2/dx 2, α > -1, in the space L 2(ℝ) with weight |x| αp(x). As is well known, the answer to this problem in the case p(x) ≡ 1 is positive; it was obtained by using delicate methods of the theory of Hilbert spaces with indefinite metric. The use of a general similarity criterion in combination with methods of perturbation theory for differential operators allows us to generalize this result to a much wider class of weight functions p(x).
  • Digital Object Identifier (doi)

    Author List

  • Faddeev MM; Shterenberg RG
  • Start Page

  • 261
  • End Page

  • 270
  • Volume

  • 72
  • Issue

  • 1-2