Convergence of a Class of Generalized Sampling Kantorovich Operators Perturbed by Multiplicative Noise

In this paper a new family of sampling type series is introduced. From the mathematical point of view, the present definition generalizes the notion of the well-known sampling Kantorovich operators, in fact providing a weighted version of the original family of operators by functions gk,w, k∈ ℤ, w > 0, called noise functions. From the application point of view, this situation represents the reconstruction problem of signals perturbed by linear or nonlinear multiplicative noise sources. In this respect, approximation results have been established in various contexts. First, pointwise and uniform approximation theorems have been proved. Then, convergence theorems have been derived in the general setting of Orlicz spaces. The latter context allows us to deduce, in particular, an Lp-convergence theorem. Finally, the concept of delta convergent sequence is introduced and also used in order to prove that the above family of sampling type operators extend the well-known generalized sampling series of P.L. Butzer.