A strong converse inequality for generalized sampling operators

We establish a two-term strong converse inequality for the rate of approximation of generalized sampling operators by means of the classical moduli of smoothness. It matches an already known direct estimate. We combine the direct and the converse estimates to derive the saturation property and class of this approximation operator. We demonstrate the general results for the sampling operators generated by the central B-splines, linear combinations of translates of B-splines, and the Bochner–Riesz kernel.