Israel Journal of Mathematics

, Volume 10, Issue 3, pp 364–372 | Cite as

Norm inequalities for a certain class of ∞ functions

  • I. J. Schoenberg


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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    J. D. Buckholtz,The Whittaker constant and successive derivatives of entire functions, J. Approximation Theory,3 (1970), 194–212.MATHCrossRefMathSciNetGoogle Scholar
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    I. J. Schoenberg,On the zeros of successive derivatives of integral functions, Trans. Amer. Math. Soc.,40 (1936), 12–23.MATHCrossRefMathSciNetGoogle Scholar
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    J. M. Whittaker,Interpolatory function theory, Cambridge University Press, 1935.Google Scholar

Copyright information

© Hebrew Univeristy 1971

Authors and Affiliations

  • I. J. Schoenberg
    • 1
  1. 1.Mathematics Research CenterUniversity of WisconsinMadison

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