标题： 关于一类广义Sturm-Liouville算子的特征值界 显示英文标题

标题： On eigenvalue bounds for a general class of Sturm-Liouville operators

摘要： 我们考虑带测度值权重和势函数的Sturm-Liouville算子，以及正有界扩散系数且远离零。通过局部周期性条件（可以看作定量的Gordon条件），我们证明了对应于$L_p$和$1\leq p<\infty$的算子的特征值界的估计。我们还解释了该定量界的确切性，并给出了拟周期算子的一个例子。 显示英文摘要

摘要： We consider Sturm-Liouville operators with measure-valued weight and potential, and positive, bounded diffusion coefficient which is bounded away from zero. By means of a local periodicity condition, which can be seen as a quantitative Gordon condition, we prove a bound on eigenvalues for the corresponding operator in $L_p$, for $1\leq p<\infty$. We also explain the sharpness of our quantitative bound, and provide an example for quasiperiodic operators.