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Transactions of the American Mathematical Society

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The behavior at infinity of certain convolution transforms


Author: I. I. Hirschman
Journal: Trans. Amer. Math. Soc. 70 (1951), 1-14
MSC: Primary 42.4X
DOI: https://doi.org/10.1090/S0002-9947-1951-0041272-9
MathSciNet review: 0041272
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  • [1] I. I. Hirschman, Jr., A new representation and inversion theory for the Laplace integral, Duke Math. J. vol. 15 (1948) pp. 473-494. MR 0025616 (10:36b)
  • [2] I.I. Hirschman, Jr., and D. V. Widder, An inversion and representation theory for convolu- tion transforms with totally positive kernels, Proc. Nat. Acad. Sci. U.S.A. vol. 34 (1948) pp. 152-156. MR 0025617 (10:36c)
  • [3] -, The inversion of a general class of convolution transforms, Trans. Amer. Math. Soc. vol. 66 (1949) pp. 135-201. MR 0032817 (11:350g)
  • [4] I. J. Schoenberg, On totally positive functions, Laplace integrals, and entire functions of the Laguerre-Pólya-Schur type, Proc. Nat. Acad. Sci. U.S.A. vol. 33 (1947) pp. 11-17. MR 0018706 (8:319b)
  • [5] E. C. Titchmarsh, Introduction to the theory of Fourier integrals, Oxford University Press, 1937.
  • [6] D. V. Widder, The Laplace transform, Princeton University Press, 1941. MR 0005923 (3:232d)

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DOI: https://doi.org/10.1090/S0002-9947-1951-0041272-9
Article copyright: © Copyright 1951 American Mathematical Society

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