Israel Journal of Mathematics

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

Norm inequalities for a certain class of ∞ functions

  • I. J. Schoenberg
Article

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

  1. 1.
    R. P. Boas,Entire functions, Academic Press Inc., New York, 1954.MATHGoogle Scholar
  2. 2.
    J. D. Buckholtz,The Whittaker constant and successive derivatives of entire functions, J. Approximation Theory,3 (1970), 194–212.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    I. J. Schoenberg,On the zeros of successive derivatives of integral functions, Trans. Amer. Math. Soc.,40 (1936), 12–23.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    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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