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Universal truncation error upper bounds in sampling restoration. (English) Zbl 1203.94082

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.

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
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