A perturbed Whittaker–Kotelʼnikov–Shannon sampling theorem

The sampling theorem of Whittaker (1915) [31], , Kotelʼnikov (1933) [25], and Shannon (1949) [28] gives cardinal series representations for finite L2-Fourier transforms at equidistant sampling points. Here we investigate the situation when the Fourier transform is replaced by a perturbed one. Thus the kernel of the transform will be of the form exp(−ixt)+ε(x,t), instead of exp(−ixt) in the unperturbed case. The perturbed kernel arises from first order eigenvalue problems with rank one perturbations.