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Let f be a real entire function of order one, normal type that is bounded on the real axis and L = (D), D = (d/dz) with q(co) a Laguerre-Polya function satisfying qp(O) = 0. Then the final set of f with respect to L is contained in the real axis as either a discrete subset or the whole axis.

Final sets for operators on real entire functions of order one, normal type