标题： 一维Schrödinger算子的奇点和共振的渐近分布 显示英文标题

标题： Singularities and asymptotic distribution of resonances for Schrödinger operators in one dimension

摘要： 我们得到了关于一维薛定谔算子共振的高能分布的新结果。 我们的主要结果是以位势的奇异支集为界，在高于任意对数曲线的共振密度上给出了一个上界。 我们还证明了关于远离实轴扇形区域内的共振分布的结果，并构造了一类位势，这些位势沿着不同的对数曲线产生多个共振序列，明确计算出这些共振的渐近位置。 这些结果通过反射系数的积分表示法统一起来。 显示英文摘要

摘要： We obtain new results about the high-energy distribution of resonances for the one-dimensional Schr\"odinger operator. Our primary result is an upper bound on the density of resonances above any logarithmic curve in terms of the singular support of the potential. We also prove results about the distribution of resonances in sectors away from the real axis, and construct a class of potentials producing multiple sequences of resonances along distinct logarithmic curves, explicitly calculating the asymptotic location of these resonances. The results are unified by the use of an integral representation of the reflection coefficients.