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 thatf(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) off(t) on −T, T] is less than δ we can extrapolate the values off(t) on the interval −A, A] such that the difference between the extrapolated value and the exact value off(t) does not exceed ε.