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