The paper concerns problems of the recovery of differential operators from a noisy Fourier transform. In particular, optimal methods are obtained for the recovery of powers of generalized Laplace operators from a noisy Fourier transform in the $L_2$-metric.

翻译：本文研究从带噪傅里叶变换恢复微分算子的问题。具体而言，在$L_2$度量下，获得了从带噪傅里叶变换恢复广义拉普拉斯算子幂次的最优方法。