On the Optimal Recovery of One Family of Operators on a Class of Functions from Approximate Information about Its Spectrum
摘要
We find explicit expressions for optimal recovery methods in the problemof recovering the values of continuous linear operators on a Sobolev function classfrom the following information: The Fourier transform of functions is known approximatelyon some measurable subset of the finite-dimensional space on which the functions aredefined. As corollaries, we obtain optimal methods for recovering the solution to the heatequation and solving the Dirichlet problem for a half-space.