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1.
  • Kurasov, Pavel, et al. (författare)
  • On the essential spectrum of a class of singular matrix differential operators. II. Weyl's limit circles for the Hain-Lust operator whenever quasi-regularity conditions are not satisfied
  • 2008
  • Ingår i: Proceedings of the Royal Society of Edinburgh: Section A Mathematics. - Cambridge University Press. - 0308-2105. ; 138:1, s. 109-138
  • Tidskriftsartikel (refereegranskat)abstract
    • The essential spectrum of the singular matrix differential operator of mixed order determined by the operator matrix GRAPHICS is studied. Investigation of the essential spectrum of the corresponding self-adjoint operator is continued but; now without assuming that the quasi-regularity conditions are satisfied. New conditions that guarantee that the operator is semi-bounded from below are derived. It is proven that the essential spectrum of any self-adjoint operator associated with the matrix differential operator is given by the range range((mp - beta(2))/px(2)) in the case where the quasi-regularity conditions are not satisfied.
2.
  • Kurasov, Pavel, et al. (författare)
  • Wigner-von Neumann perturbations of a periodic potential: spectral singularities in bands
  • 2007
  • Ingår i: Mathematical Proceedings of the Cambridge Philosophical Society. - Cambridge University Press. - 0305-0041. ; 142:1, s. 161-183
  • Tidskriftsartikel (refereegranskat)abstract
    • Wigner-von Neumann type perturbations of the periodic one-dimensional Schrodinger operator are considered. The asymptotics of the solution to the generalized eigenfunction equation is investigated. It is proven that a subordinated solution and therefore art embedded eigenvalue may occur at the points of the absolutely continuous spectrum satisfying a certain resonance (quantization) condition between the frequencies of the perturbation, the frequency of the background potential and the corresponding quasimomentum.
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refereegranskat (2)
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