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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A short proof of Schoenberg’s theorem
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by Paul Ressel PDF
Proc. Amer. Math. Soc. 57 (1976), 66-68 Request permission

Abstract:

Using positive semidefiniteness of Laplace transforms, we give a short and simple proof of Schoenberg’s theorem characterising radially symmetric positive semidefinite functions on a Hilbert space. A slight generalisation of this theorem is also given.
References
    W. F. Donoghue, Distributions and Fourier transforms, Academic Press, New York, 1969.
  • Paul Ressel, Laplace-Transformation nichtnegativer und vektorwertiger Maße, Manuscripta Math. 13 (1974), 143–152 (German, with English summary). MR 344886, DOI 10.1007/BF01411492
    • I. J. Schoenberg, Metric spaces and completely monotone functions, Ann. of Math. 39 (1938).
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 57 (1976), 66-68
  • MSC: Primary 44A10
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0405007-2
  • MathSciNet review: 0405007