Abstract Boundary value problems for a second-order ordinary differential equation with a nonsmooth potential are considered. An asymptotic representation for an operator semigroup is established based on a previously derived theorem on the eigenvalue asymptotics for the Hill operator. This semigroup is used to describe weak solutions of a mixed problem for a parabolic equation.

中文翻译：

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带有希尔算子的混合问题的傅里叶方法

摘要 考虑了具有非光滑势的二阶常微分方程的边值问题。算子半群的渐近表示是基于先前导出的关于希尔算子的特征值渐近的定理而建立的。该半群用于描述抛物线方程混合问题的弱解。