Time shifted aliasing error upper bounds for truncated sampling cardinal series

Time shifted aliasing error upper bound extremals for the sampling reconstruction procedure are fully characterized. Sharp upper bounds are found on the aliasing error of truncated cardinal series and the corresponding extremals are described for entire functions from certain specific Lp, p>1, classes. Analogous results are obtained in multidimensional regular sampling. Truncation error analysis is provided in all cases considered. Moreover, sharpness of bounding inequalities, convergence rates and various sufficient conditions are discussed.