Universal truncation error upper bounds in sampling restoration

Abstract

Universal (pointwise uniform and time shifted) truncation error upper bounds are presented for the Whittaker--Kotel'nikov--Shannon (WKS) sampling restoration sum for Bernstein function classes $B_{\pi ,d}^q,q>1,d\in \mathbb{N}$, when the decay rate of the sampled functions is unknown. The case of regular sampling is discussed. Extremal properties of related series of sinc functions are investigated.

18 pages, 2 figures. This is an Author's Accepted Manuscript of an article published in the Georgian Mathematical Journal. Vol.17, No. 4. (2010), 765-786. The final publication is available at De Gruyter. DOI: 10.1515/gmj.2010.033

Cited by in corpus (2)

• Universal truncation error upper bounds in irregular sampling restoration
• Average sampling restoration of harmonizable processes