Approximation by multivariate Kantorovich-Kotelnikov operators

Approximation properties of multivariate Kantorovich-Kotelnikov type operators generated by different band-limited functions are studied. In particular, a wide class of functions with discontinuous Fourier transform is considered. The $L_p$-rate of convergence for these operators is given in terms of the classical moduli of smoothness. Several examples of the Kantorovich-Kotelnikov operators generated by the $\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{c}$-function and its linear combinations are provided.