On real-analytic recurrence relations for cardinal exponential B-splines

Let LN+1 be a linear differential operator of order N+1 with constant coefficients and real eigenvalues λ1,…,λN+1, let E(ΛN+1) be the space of all C∞-solutions of LN+1 on the real line. We show that for N⩾2 and n=2,…,N, there is a recurrence relation from suitable subspaces En to En+1 involving real-analytic functions, and with EN+1=E(ΛN+1) if and only if contiguous eigenvalues are equally spaced.