응용수학세미나
연사 : 이영란박사(KAIST)
제목 : "Bethe-Sommerfeld conjecture on polyharmonic operator
with limit-periodic potent"
일시 : 2007.9.13(목), 오후4:30
장소 : 산업경영학동 3221호
요약 : We consider spectral properties of a polyharmonic operator $H=(-\Delta)^l+V(x)$ with a limit-periodic potential $V(x)$ in dimension two with $l \geq 6, l \in \Z$. 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 corresponding to this region are close to plane waves $e^{i\langle \vec k,\vec x\rangle }$. 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). Joint work with Yulia Karpeshina