Convergence of a class of generalized sampling Kantorovich operators perturbed by multiplicative noise (Q6601631)

In this article a 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 noice functions. From the application point of view, this situation represents the reconstruction problem of signals perturbed by linear or nonlinear multiplicative noise sources. First, pointwise and uniform approximation theorems have been proved. Then, convergence theorems have been derived in the general setting of Orlicz spaces. Also, an \(L_p\)-convergence theorem is established. 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.\N\NFor the entire collection see [Zbl 1515.46001].