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
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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).
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