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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On special classes of entire functions whose zeros and growth are restricted


Author: Carl L. Prather
Journal: Trans. Amer. Math. Soc. 258 (1980), 181-189
MSC: Primary 30D15
DOI: https://doi.org/10.1090/S0002-9947-1980-0554327-5
MathSciNet review: 554327
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Abstract: The present paper is an investigation of the uniform limits on bounded sets of entire functions of genus $ \leqslant \,2p$ whose zeros are real, or lie in an even number of sectors (or correspondingly on rays) of a certain size, both the number and size depending on p. A characterization of the uniform limits of entire functions of genus $ \leqslant \,2p$ whose zeros lie in these sectors is given.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1980-0554327-5
Keywords: Real entire functions, finite genus, uniform approximation on bounded sets (discs)
Article copyright: © Copyright 1980 American Mathematical Society