The extrapolation of band-limited signals in L² with sampling errors

In this paper we will provide a theory for an extrapolation algorithm of band-limited signals with sampling errors or low noises. The main result is as follows: Suppose that f(t) is in L² and is a continuous Ω band-limited signal. Then for any positive numbers T, A(>T) and ε, there exists a δ>0 such that when the sampling errors (or noises) of f(t) on [−T, T] is less than δ we can extrapolate the values of f(t) on the interval [−A, A] such that the difference between the extrapolated value and the exact value of f(t) does not exceed ε.