Uniform bounds of truncation error for shannon sampling expansion

Abstract

Let B^pΩ, 1 ≤ p ≤ 8; be the set of all bounded functions from L^p(ℝ) which can be extended to entire functions of exponential type ℝ. The uniform bounds for truncation error of Shannon sampling expansion from local averages are obtained for functions f ∈ B^pΩ with the decay condition equation where A and δ are positive constants. Furthermore we also establish similar results for non-bandlimit functions from Besov classes with the same decay condition as above.