Geodesic
Uniform Approximation by Polynomials with Variable Exponents
Canadian journal of mathematics, Tome 35 (1983) no. 3, pp. 547-557

Voir la notice de l'article provenant de la source Cambridge University Press

We examine questions related to approximating functions by sums of the form We focus on approximations to functions given by the integral transformation where γ is a positive measure. Approximations to this class of functions (Laplace transforms in the variable — lnx) are particularly well behaved (see Theorem 1). Questions concerning existence, uniqueness and characterization of such approximations have been thoroughly examined in the equivalent setting of exponential sum approximations (see [3], [4], [6] and [9]). Less well studied is the order of convergence of the approximation. This is the problem we address. Part of the motivation for using sums of the form (1), which we shall call Gaussian sums, stems from the observation that all analytic functions with Taylor series expansion having positive coefficients are of the form (2). 
Borwein, Peter B. Uniform Approximation by Polynomials with Variable Exponents. Canadian journal of mathematics, Tome 35 (1983) no. 3, pp. 547-557. doi: 10.4153/CJM-1983-031-7
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