Uniform Truncation Error for Shannon Sampling Expansion

Let B_Ω^p, 1 ≤ p ≤ ∞, be the set of all bounded functions from L^p(R) which can be extended to entire functions of exponential type Ω. The uniform bounds for truncation error of Shannon sampling expansion from local averages are obtained for functions f ∈ B_Ω^p with the decay condition |f(t)|≤ A/(|t|^δ), t≠0, 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.