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Proceedings of the American Mathematical Society

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


Author: C. L. Prather
Journal: Proc. Amer. Math. Soc. 90 (1984), 363-369
MSC: Primary 30D15; Secondary 30C15
DOI: https://doi.org/10.1090/S0002-9939-1984-0728349-4
MathSciNet review: 728349
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0728349-4
Keywords: Real entire function, exponential type, final set, differential operator
Article copyright: © Copyright 1984 American Mathematical Society

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