Closure theorems with applications to entire functions with gaps

Anderson, J. M.; Binmore, K. G.

doi:10.1090/S0002-9947-1971-0289141-6

Closure theorems with applications to entire functions with gaps
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by J. M. Anderson and K. G. Binmore PDF

Trans. Amer. Math. Soc. 161 (1971), 381-400 Request permission

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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