Olenko, Andriy Ya.; Pogány, Tibor K. Universal truncation error upper bounds in sampling restoration. (English) Zbl 1203.94082 Georgian Math. J. 17, No. 4, 765-786 (2010). Summary: Universal (pointwise uniform and time shifted) truncation error upper bounds are presented for the Whittaker-Kotel’nikov-Shannon sampling restoration sum for Bernstein function classes \(B^q_{\pi,d}, q > 1, d \in \mathbb N\), when the decay rate of the sample functions is unknown. The case of regular sampling is discussed. Extremal properties of the related series of sinc functions are investigated. Cited in 3 Documents MSC: 94A20 Sampling theory in information and communication theory 41A25 Rate of convergence, degree of approximation 41A05 Interpolation in approximation theory 41A17 Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities) 41A80 Remainders in approximation formulas 26D15 Inequalities for sums, series and integrals Keywords:Whittaker-Kotel’nikov-Shannon sampling restoration formula; approximation/interpolation error level; Plancherel-Pólya inequality; Bernstein function class; regular sampling theorem; truncation error upper bound; multidimensional sampling; sinc functions; incomplete lambda function PDFBibTeX XMLCite \textit{A. Ya. Olenko} and \textit{T. K. Pogány}, Georgian Math. J. 17, No. 4, 765--786 (2010; Zbl 1203.94082) Full Text: DOI arXiv