Asymptotic Formulae for Linear Combinations of Generalized Sampling Operators

Abstract

We give some Voronovskaja formula for linear combinations of generalized sampling operators and we furnish also a quantitative version in terms of the classical Peetre $K$-functional. This provides a better order of approximation in the asymptotic formula. We apply the general theory to various kernels: Bochner-Riesz kernel, translates of B-splines and Jackson type kernel.