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<p<∞, can be represented as

$f(x) = \mathop \Sigma \limits_{j \in z} f(j\pi /\sigma )\tfrac{{sin\sigma (x - j\pi /\sigma )}}{{\sigma (x - j\pi /\sigma )}}, \sigma > 0$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
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