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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Closure theorems with applications to entire functions with gaps


Authors: J. M. Anderson and K. G. Binmore
Journal: Trans. Amer. Math. Soc. 161 (1971), 381-400
MSC: Primary 90.57
MathSciNet review: 0289141
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Abstract: In this paper we consider questions of completeness for spaces of continuous functions on a half line which satisfy appropriate growth conditions. The results obtained have consequences in the theory of entire functions with gap power series. In particular we show that, under an appropriate gap hypothesis, the rate of growth of an entire function in the whole plane is determined by its rate of growth along any given ray.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0289141-6
PII: S 0002-9947(1971)0289141-6
Keywords: Banach space, entire function, closure, approximation, power series
Article copyright: © Copyright 1971 American Mathematical Society