The paper concerns problems of the recovery of linear operators defined on sets of functions from information of these functions given with stochastic errors. The constructed optimal recovery methods, in general, do not use all the available information. As a consequence, optimal methods are obtained for recovering derivatives of functions from Sobolev classes by the information of their Fourier transforms given with stochastic errors. A similar problem is considered for solutions of the heat equation.

翻译：本文研究在给定具有随机误差的函数信息下，定义在函数集上的线性算子的恢复问题。所构建的最优恢复方法通常不会利用所有可用信息。基于此，得到了从具有随机误差的傅里叶变换信息中恢复索伯列夫类函数导数的最优方法。对于热方程的解也考虑了类似的问题。