On polyharmonic operators with limit-periodic potential in dimension two

Academic Article


  • This is an announcement of the following results. We consider a polyharmonic operator H = (-Δ) l + V(x) in dimension two with l ≥ 6 and V(x) being a limit-periodic potential. We prove that the spectrum of H contains a semiaxis and there is a family of generalized eigenfunctions at every point of this semiaxis with the following properties. First, the eigenfunctions are close to plane waves at the high-energy region. Second, the isoenergetic curves in the space of momenta corresponding to these eigenfunctions have the form of slightly distorted circles with holes (Cantor-type structure). Third, the spectrum corresponding to the eigenfunctions (the semiaxis) is absolutely continuous. © 2006 American Mathematical Society.
  • Digital Object Identifier (doi)

    Author List

  • Karpeshina Y; Lee YR
  • Start Page

  • 113
  • End Page

  • 120
  • Volume

  • 12