Error estimates for a class of integral and discrete transforms (Q2754971)

The paper is concerned with the study of a class of integral transforms, the kind of \(\mathcal{F}(f;t):=\int\limits_{a}^{b}F(x,t)f(x)w(x)dx\), which generalize the classical Fourier transform, since they verify a property which is an analogue of the formal property of the classical operator see \textit{C.Belingeri} and \textit{P.E.Ricci} [Riv. Mat. Univ. Parma, V Ser., 1, 333-338 (1992; Zbl 0839.42007)], [Rend. Mat. Appl., VII Ser. 14, No. 1, 145-158 (1994; Zbl 0805.42007)]. The estimates for global error are given in terms of the best approximation error. The global error is defined by: \(\mathcal{\epsilon }_{m}(f;t):=\mid\;\mathcal{F} (f;t) - \widetilde{\mathcal{F}}_{m}(f;t) \mid\), where \(\widetilde{\mathcal{F}}_{m}(f;t)\) denotes the approximation for the integral transform.