Optimal Reconstruction of the Solution of the Wave Equation from Inaccurate Initial Data

In the present paper, we consider the problem of the optimal reconstruction of the solution of the wave equation from the approximate values of the Fourier coefficients of the function specifying the initial form of the string. For an operator defined on the weight space of vectors from $l_2$, we present the solution of the more general problem of reconstruction from the approximate values of the coordinates of these vectors.