An application of the sampling theorem

Let B_σ,p,1 <-p<-∞, be the set of all functions from L₈(R) which can be continued to entire functions of exponential type <-σ. The well known Shannon sampling theorem and its generalization 1] state that every f∈B_σ,p, 1 $$f(x) = \mathop \Sigma \limits_{j \in z} f(j\pi /\sigma )\tfrac{{sin\sigma (x - j\pi /\sigma )}}{{\sigma (x - j\pi /\sigma )}}, \sigma > 0$$ It is well known that the Shannon sampling theorem plays an important role in many applied fields 1,2,7]. In this paper we give an application of sampling theorem to approximation theory.