Some problems of coding and restoring functions (Q1176883)

The questions of coding and subsequently restoring functional dependence are of interest from both theoretical and applied points of view. This is explained, in particular, by the fact that effective methods of solution of extremal problems developed in the theory of approximation also permit a construction of exact solutions of a number of problems of optimal coding and restoration of functions. In the articles that study these problems the method of coding is estimated from the error of the restoration of the coded function itself. And in this paper a more general problem is studied, where discrete information about a function \(u\) is used to reconstruct a function \(f=Au\), which is the image of a function \(u\) under some operator \(A\). The concrete cases of differentiation and convolution operators and the case of a solution of a boundary value problem are also considered.