On the optimal constants in the two-sided Stechkin inequalities
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We address the optimal constants in the strong and the weak Stechkin inequalities which appear in the characterization of approximation spaces which arise from sparse approximation. An elementary proof of a constant given by Bennett is provided, and we improve the constants given by Stechkin and Copson. By means of convex optimization, we compute two decimal places of the optimal constant in the classical version. Finally, the minimal constants in the weak Stechkin inequality are presented.
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