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Proof of a conjecture of I. J. Schoenberg


Author: I. I. Hirschman
Journal: Proc. Amer. Math. Soc. 1 (1950), 63-65
MSC: Primary 27.0X
DOI: https://doi.org/10.1090/S0002-9939-1950-0032705-7
MathSciNet review: 0032705
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  • [1] I. I. Hirschman, Jr., and D. V. Widder, An inversion and representation theory for convolution transforms with totally positive kernels, Proc. Nat. Acad. Sci. U. S. A. vol. 34 (1948) pp. 152-156. MR 0025617 (10:36c)
  • [2] I. J. Schoenberg, On totally positive functions, Laplace integrals and entire functions of the Laguerre-Pölya-Schur type, Proc. Nat. Acad. Sci. U. S. A. vol. 33 (1947) pp. 11-17. MR 0018706 (8:319b)
  • [3] G. P61ya, and N. Wiener, On the oscillation of the derivatives of a periodic function, Trans. Amer. Math. Soc. vol. 52 (1942) pp. 249-256. MR 0007169 (4:97a)
  • [4] G. Szegö, On the oscillation of differential transforms. I, Trans. Amer. Math. Soc. vol. 52 (1942) pp. 450-462. MR 0007170 (4:97b)

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DOI: https://doi.org/10.1090/S0002-9939-1950-0032705-7
Article copyright: © Copyright 1950 American Mathematical Society

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