势能解析依赖于能量的Hill算子
Hill's operators with the potentials analytically dependent on energy
摘要：
我们考虑线上的薛定谔算子，其势关于坐标变量是周期性的，关于能量变量是实解析的。证明了如果势的虚部在右半平面内有界，则高能谱是实的，并确定了相应的渐近性。此外，Dirichlet和Neumann问题被考虑。这些结果被用来分析良好的Boussinesq方程。
英文摘要：
We consider Schrödinger operators on the line with potentials that are periodic with respect to the coordinate variable and real analytic with respect to the energy variable. We prove that if the imaginary part of the potential is bounded in the right half-plane, then the high energy spectrum is real, and the corresponding asymptotics are determined. Moreover, the Dirichlet and Neumann problems are considered. These results are used to analyze the good Boussinesq equation.
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