论文标题
在与幂律奇点的绝对连续措施的傅里叶渐近学上
On the Fourier asymptotics of absolutely continuous measures with power-law singularities
论文作者
论文摘要
我们证明了对某些绝对连续措施的傅立叶变换的平方绝对值的时间平均值，这些措施可能具有幂律奇异性，从某种意义上说，它们的radon-nikodym衍生物与幂律顺序不同。我们还讨论了离散laplacian的有限级扰动光谱测量的应用。
We prove sharp estimates on the time-average behavior of the squared absolute value of the Fourier transform of some absolutely continuous measures that may have power-law singularities, in the sense that their Radon-Nikodym derivatives diverge with a power-law order. We also discuss an application to spectral measures of finite-rank perturbations of the discrete Laplacian.
