Universal truncation error upper bounds in sampling restoration

作者：Olenko Andriy Ya^*; Pogany Tibor K

来源：Georgian Mathematical Journal, 2010, 17(4): 765-786.

DOI：10.1515/GMJ.2010.033

• Whittaker-Kotel'nikov Shannon sampling restoration formula
• approximation/interpolation error level
• Plancherel-Polya inequality
• Bernstein function class
• regular sampling theorem
• truncation error upper bound
• multidimensional sampling
• sinc functions
• incomplete Lambda function

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(pi)(,d)(q), q > 1, d is an element of 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.

• 出版日期2010