Abstract
In 1936 the author showed that the function sin(π(x+1)/4) is the entire function of least exponential type (=π/4) among all entire functionsf(z) with the property thatf (n)(z) vanishes somewhere in the real interval [−1, 1] (n=0, 1,2,…). Now more precise results of this kind are obtained by working within the class ∞[−1, 1].
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References
R. P. Boas,Entire functions, Academic Press Inc., New York, 1954.
J. D. Buckholtz,The Whittaker constant and successive derivatives of entire functions, J. Approximation Theory,3 (1970), 194–212.
I. J. Schoenberg,On the zeros of successive derivatives of integral functions, Trans. Amer. Math. Soc.,40 (1936), 12–23.
J. M. Whittaker,Interpolatory function theory, Cambridge University Press, 1935.
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For Paul Montel on his 95th birthday
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Schoenberg, I.J. Norm inequalities for a certain class of ∞ functions. Israel J. Math. 10, 364–372 (1971). https://doi.org/10.1007/BF02771654
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DOI: https://doi.org/10.1007/BF02771654