On sharp bounds for remainders in multidimensional sampling theorem (CROSBI ID 132360)
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Olenko, Andriy Yakovich ; Poganj, Tibor
engleski
On sharp bounds for remainders in multidimensional sampling theorem
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 Cram\'er 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.
Interpolation error ; extremal function ; multidimensional sampling theorem ; WKS sampling formula ; Paley-Wiener function class ; Frechet - (semi-) variation ; weak Cramer random fields
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