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On sharp bounds for remainders in multidimensional sampling theorem. (English) Zbl 1156.94324

Summary: Sharp upper bounds for interpolation remainders of the multidimensional Paley-Wiener function class 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 the extensive reference list are given concerning truncation error upper bounds for deterministic and random signal functions. Finally new research directions are posed and discussed.

MSC:

94A20 Sampling theory in information and communication theory
60G12 General second-order stochastic processes
26D15 Inequalities for sums, series and integrals
30D15 Special classes of entire functions of one complex variable and growth estimates
41A05 Interpolation in approximation theory
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