Fourier integrals and metric geometry
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- by J. von Neumann and I. J. Schoenberg
- Trans. Amer. Math. Soc. 50 (1941), 226-251
- DOI: https://doi.org/10.1090/S0002-9947-1941-0004644-8
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References
- P. Lévy, Calcul des Probabilités, Paris, 1925.
K. Menger, Die Metrik des Hilbertschen Raumes, Anzeiger der Akademie der Wissenschaften in Wien, Mathematisch-Naturwissenschaftliche Klasse, vol. 65 (1928), pp. 159-160.
- I. J. Schoenberg, Remarks to Maurice Fréchet’s article “Sur la définition axiomatique d’une classe d’espace distanciés vectoriellement applicable sur l’espace de Hilbert” [MR1503246], Ann. of Math. (2) 36 (1935), no. 3, 724–732. MR 1503248, DOI 10.2307/1968654
- I. J. Schoenberg, Metric spaces and positive definite functions, Trans. Amer. Math. Soc. 44 (1938), no. 3, 522–536. MR 1501980, DOI 10.1090/S0002-9947-1938-1501980-0
- I. J. Schoenberg, Metric spaces and completely monotone functions, Ann. of Math. (2) 39 (1938), no. 4, 811–841. MR 1503439, DOI 10.2307/1968466 M. H. Stone, Linear transformations in Hilbert space III, Proceedings of the National Academy of Sciences, vol. 16 (1930), pp. 172-175.
- M. H. Stone, On one-parameter unitary groups in Hilbert space, Ann. of Math. (2) 33 (1932), no. 3, 643–648. MR 1503079, DOI 10.2307/1968538
- W. A. Wilson, On Certain Types of Continuous Transformations of Metric Spaces, Amer. J. Math. 57 (1935), no. 1, 62–68. MR 1507055, DOI 10.2307/2372019
Bibliographic Information
- © Copyright 1941 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 50 (1941), 226-251
- MSC: Primary 42.4X
- DOI: https://doi.org/10.1090/S0002-9947-1941-0004644-8
- MathSciNet review: 0004644