Truncation Error Bound for the Kravchenko–Kotelnikov Series

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 Fa(t) of the atomic function ha(x), linearly transformed with respect to the argument. In this case, the function Fa(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 Fa(t) is replaced by a partial one is considered. A comparative analysis of the obtained formulae is carried out.