Fourier integrals and metric geometry

By J. Neumann, I. J. Schoenberg. 1941

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On the Schoenberg Transformations in Data Analysis: Theory and Illustrations (2010, background): “The transformation of a line is called “screw line” by Von Neumann and Schoenberg (1941), and “helix” by Kolmogorov (1940) - an adequate terminology in view of Figure 2.”
Jensen-Shannon divergence and Hilbert space embedding (2004, methodology): “For = 0, the -spirals become helixes as studied by Kolmogorov [6] and von Neumann and Schoenberg, [ 14 ].”
Geometric embeddings of metric spaces (2003, methodology): “Definite functions on metric spaces were introduced long ago by Schoenberg and von Neumann (3)[58], [78], who studied isometric embeddability of metric spaces in Hilbert spaces via Fourier analysis.”
On the characteristics of a class of Gaussian processes within the white noise space setting (2009, background): “Functions r such that the kernel K r ( t, s ) is positive have been characterized by von Neumann and Schoenberg when r is real; see [34, Theorem 1, p. 229].”
Interpolation of scattered data: Distance matrices and conditionally positive definite functions (1986, result): “When k = 1, this result was observed by von Neumann and Schoenberg [22] for 9 = 89 Furthermore, by Corol lary 2.1 and the fact that (11 xi - xJl127) ~ ~r for 0 < ~" < 1, we see that (1 + I lxl l ' ) -~ is strictly positive definite for/z > 0, 0 ,r 2.”