Given a bandlimited function f on R. By regularizing the usual Whitaker-Kotel’Nikov-Shannon sampling principle with a scaled-truncated Gaussian, one can show that the finite cardinal series of compactly converges to f with an exponential decay rate in terms of the number of sampling points. This is an essential result for my work “Superiority of GNNs (Graph Neural Networks) over NNs (Neural Networks) in generalizing bandlimited functions”, in which the said regularized sampling principle was shown to be realized by a GNN structure.
https://univienna.zoom.us/j/64895816787?pwd=L0tHVnBPUkJFQVVSR3Y2QnhVRXRGZz09