Whittaker-Hill方程与半有限隙Schroedinger算子
Whittaker-Hill equation and semifinite-gap Schroedinger operators
摘要：
一个周期性的一维薛定谔算子被称为半有限间隙，如果它的谱中的每一个第二间隙最终关闭。通过对Whittaker-Hill方程应用Darboux变换，我们构造了三角函数中半有限间隙Schroedinger算子的显式例子。我们给出了相应势的正则性判据，并研究了新算子的谱性质。
英文摘要：
A periodic one-dimensional Schroedinger operator is called semifinite-gap if every second gap in its spectrum is eventually closed. We construct explicit examples of semifinite-gap Schroedinger operators in trigonometric functions by applying Darboux transformations to the Whittaker-Hill equation. We give a criterion of the regularity of the corresponding potentials and investigate the spectral properties of the new operators.
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