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Abstract
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 , q > 1, d ∈ 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.
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
Received: 2008-11-07
Revised: 2009-06-11
Published Online: 2010-10-21
Published in Print: 2010-December
© de Gruyter 2010