Sampling theorem for entire functions of exponential growth (Q5957148)

A generalization of Shannon's sampling theorem is obtained for entire functions satisfying \(|F(z)|\leq C\exp\{L|z|^{1/s}+a|\text{ Im}(z)|\}\), where \(C, L, a\), and \(s\) are constants and \(s>1\). The sampling functions belong to a Gevrey class of order \(r\) \((1<r<s\)). Error estimates depending on the sampling functions and the sampling sequence are included. Finally the theory is applied to functions satisfying the heat equation.