Whittaker–Kotelnikov–Shannon Sampling Theorem and Aliasing Error Original Research Article

LetBσ, p, 1⩽p⩽∞, be the set of all functions fromLp(R) which can be continued to entire functions of exponential type ⩽σ. The well known Whittaker–Kotelnikov–Shannon sampling theorem states that everyf∈Bσ, 2can be represented as[formula]in normL2(R). We prove that it is also true for allf∈Bσ, p, 1