Universal truncation error upper bounds in sampling restoration

Andriy Ya. Olenko; Tibor K. Pogány

doi:10.1515/gmj.2010.033

Published by De Gruyter October 21, 2010

Universal truncation error upper bounds in sampling restoration

Andriy Ya. Olenko and Tibor K. Pogány

From the journal Georgian Mathematical Journal

https://doi.org/10.1515/gmj.2010.033

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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

Universal truncation error upper bounds in sampling restoration

Abstract

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