Let LN+1 be a linear differential operator of order N + 1 with constant coefficients
and real eigenvalues λ 1, ..., λ N+1, let E( N+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 εn to εn+1 involving real-analytic functions, and
with εN+1 = E(Λ N+1) if and only if contiguous eigenvalues are equally spaced.
