05-26 Yulia Karpeshina and Young-Ran Lee
Spectral Properties of a Polyharmonic Operator with Limit Periodic Potential in Dimension Two (an announcement). (317K, ps) Jan 20, 05
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Abstract. We consider a polyharmonic operator $H=(-\Delta)^l+V(x)$ in dimension two with $l>5$ 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 a form of a distorted circles with holes (Cantor type structure). Third, the spectrum corresponding to the eigenfunctions (the semiaxis) is absolutely continuous.

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