The characterization of the derivatives for linear combinations of Post-Widder operators in \(L_p\)
The Post-Widder operators constitue inversion formulas for the Laplace transform. \textit{Z. Ditzian} and \textit{V. Totik} [Modulus of smoothness (1987; Zbl 0666.41001)] proved direct and converse results for the rates of convergence for certain linear combinations of Post-Widder operators. The theorems relate the convergence of the operators with a modulus of smoothness of the function. Among other results, this detailed work extends the Ditzian-Totik results to characterize the global rate of weighted \(L_p\) \(( 1\leq p\leq \infty)\) approximation of derivatives by corresponding derivatives of linear combinations of Post-Widder operators.
scientific article; zbMATH DE number 1278843