On Sharp Bounds for Remainders in Multidimensional Sampling Theorem

Sharp upper bounds for interpolation remainders of the multidimensional Paley-Wiener class functions by finite regular Whittaker-Kotel’nikov-Shannon sampling sum are obtained. The extremal functions are given for which the derived bounds are attained. Truncation error analysis and convergence rate is provided in weak Cramer class random fields. The historical background, the development, and extensive reference list are given concerning truncation error upper bounds for deterministic and random signal functions. Finally, new research directions are posed and discussed.