Approximation of isolated eigenvalues of general singular ordinary differential operators

Academic Article


  • Let A be a self-adjoint operator defined by a general singular ordinary differential expression τ on an interval (a, b), − ∞ ≤ a < b ≤ ∞. We show that isolated eigenvalues in any gap of the essential spectrum of A are exactly the limits of eigenvalues of suitably chosen self-adjoint realizations An of τ on subintervals (an, bn) of (a, b) with an → a, bn → b. This means that eigenvalues of singular ordinary differential operators can be approximated by eigenvalues of regular operators. In the course of the proof we extend a result, which is well known for quasiregular differential expressions, to the general case: If the spectrum of A is not the whole real line, then the boundary conditions needed to define A can be given using solutions of (τ − λ)u = 0, where λ is contained in the regularity domain of the minimal operator corresponding to τ. © 1995, Birkhäuser Verlag, Basel. All rights reserved.
  • Authors

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    Digital Object Identifier (doi)

    Author List

  • Stolz G; Weidmann J
  • Start Page

  • 345
  • End Page

  • 358
  • Volume

  • 28
  • Issue

  • 3