 062 Yulia Karpeshina, YoungRan Lee
 Spectral Properties of Polyharmonic Operators with LimitPeriodic Potential in Dimension Two.
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Jan 3, 06

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Abstract. We consider a polyharmonic operator $H=(\Delta)^l+V(x)$ in
dimension two with $l\geq 6$ and a limitperiodic potential $V(x)$.
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 $e^{i\langle \vec k,\vec x\rangle }$ at the high
energy region. Second, the isoenergetic curves in the space of
momenta $\vec k$ corresponding to these eigenfunctions have a form
of slightly distorted circles with holes (Cantor type structure).
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