Title: On Sharp Bounds for Remainders in Multidimensional Sampling Theorem.
Authors: Olenko, A. Ya.; Pogány, T. K.
Abstract: 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 Cramér 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.
Subjects: INTERPOLATION; ERROR analysis in mathematics; MATHEMATICAL functions; RANDOM fields; STOCHASTIC convergence
Publication: Sampling Theory in Signal & Image Processing, 2007, Vol 6, Issue 3, p249
ISSN: 1530-6429
Publication type: Academic Journal
DOI: 10.1007/bf03549476

On Sharp Bounds for Remainders in Multidimensional Sampling Theorem.

Olenko, A. Ya.; Pogány, T. K.