Truncation Error Bound for the Kravchenko–Kotelnikov Series

Abstract

The truncation error of the Kravchenko–Kotelnikov series, which is a generalization of the Whittaker–Kotelnikov–Shannon series, is studied. The basis functions of the Kravchenko–Kotelnikov series are the spectra F_a(t) of the atomic function h_a(x), linearly transformed with respect to the argument. In this case, the function F_a(t) is defined by an infinite product. Two theorems on the truncation error bound for the Kravchenko–Kotelnikov series are proven. A practically important case in which the infinite product F_a(t) is replaced by a partial one is considered. A comparative analysis of the obtained formulae is carried out.