Super-singular Perturbations

  • Volodymyr Koshmanenko
  • Mykola Dudkin
Part of the Operator Theory: Advances and Applications book series (OT, volume 253)


In this chapter we deal with perturbations whose influence is concentrated outside of the domain of essential self-adjointness of the free Hamiltonian. We show that the extended rigged spaces method is applicable to such perturbations. A new step is the introduction of the scale of Hilbert spaces and involving in the consideration the unperturbed operator in some power. This allows one to treat perturbations with any order of singularity.


Hilbert Space Quadratic Form Singular Perturbation Symmetric Operator Spectral Theorem 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Volodymyr Koshmanenko
    • 1
  • Mykola Dudkin
    • 2
  1. 1.Institute of MathematicsNational Academy of Sciences of UkraineKyivUkraine
  2. 2.Kyiv Polytechnic InstituteNational Technical University of UkraineKyivUkraine

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