Mean sampling Kantorovich operators: approximation results and applications

As well-known, generalized sampling operators and sampling Kantorovich operators are able to approximate continuous signals and even Lp-signals in the latter case. Anyway, in the situation of a signal affected by noise, these operators are not very efficient to approximate the original signal (i.e., filtered by the noise) when the parameter goes to infinity. In order to solve this problem, we introduce a new type of operators, which we call the mean sampling Kantorovich operators. We study its approximation properties and made a comparison with the classical sampling Kantorovich operator in dealing with noisy signals.