论文标题
希尔的运营商具有分析能量的潜力
Hill's operators with the potentials analytically dependent on energy
论文作者
论文摘要
我们认为Schrödinger运算符在线上具有相对于坐标变量的周期性和相对于能量变量的真实分析的电势。我们证明，如果电势的假想部分在右半平面中有界，那么高能谱是真实的，并确定相应的渐近学。此外，还考虑了Dirichlet和Neumann的问题。这些结果用于分析良好的Boussinesq方程。
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.
