Chebyshev Approximation by Exponentials
John R. Rice · Journal of the Society for Industrial and Applied Mathematics · 1962
are considered. For n = 1 the theory is given in [3]. The principal theoretical questions of existence, uniqueness and characterization of best approximations are answered for this approximating function. The problem of the computation of best approximations is unsolved. This problem is complicated by three factors: the transcendental nature of the functions involved; the variability of the characterizing property of best approximations and the possible nonexistence of best approximations on a finite point set. In order to obtain a unified theory the approximating function E(A, x) actually considered is the set of all functions of the form