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

Prather, C. L.

doi:10.1090/S0002-9939-1984-0728349-4

Final sets for operators on real entire functions of order one, normal type
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by C. L. Prather PDF

Proc. Amer. Math. Soc. 90 (1984), 363-369 Request permission

Abstract:

Let $f$ be a real entire function of order one, normal type that is bounded on the real axis and $L = \varphi \left ( D \right )$, $D = \left ( {d / dz} \right )$ with $\varphi \left ( \omega \right )$ a Laguerre-Pólya function satisfying $\varphi \left ( 0 \right ) = 0$. 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.

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