On real-analytic recurrence relations for cardinal exponential B-splines (Q880023)

A linear differential operator \(L_{N+1}\) of order \(N+1\) with constant coefficients and real eigenvalues and the space \(E(A_{N+1})\) of all \(C^\infty\)-solutions of \(L_{N+1}\) on the real line are considered. It is shown that for \(N\geq 2\) and \(n=2,\dots,N\), there is a recurrence relation from suitable subspaces \({\mathcal E}_n\) to \({\mathcal E}_{n+1}\) involving real-analytic functions, and with \({\mathcal E}_{N+1}= E(A_{N+1})\) if and only if contiguous eigenvalues are equally spaced.