Abstract
This chapter describes several problems of approximation theory that are of interest both because of their mathematical significance and because of their importance in applications. These problems include: approximation of the derivative of noisy data, completeness of the set of products of solutions to homogeneous partial differential equation (PDE), and approximation by entire functions of exponential type. From the point of view of approximation theory, these problems are closely related to the problem of approximation of a given function by entire functions of exponential type whose Fourier transform has support inside a given convex region.
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