Schoenberg's Theorem via the law of large numbers

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dc.creatorKhoshnevisan, Davar
dc.date2005-04-29
dc.date2005-05-02
dc.date.accessioned2026-07-07T05:19:32Z
dc.date.available2026-07-07T05:19:32Z
dc.descriptionA classical theorem of S. Bochner states that a function $f:R^n \to C$ is the Fourier transform of a finite Borel measure if and only if $f$ is positive definite. In 1938, I. Schoenberg found a beautiful complement to Bochner's theorem. We present a non-technical derivation of of Schoenberg's theorem that relies chiefly on the de Finneti theorem and the law of large numbers of classical probability theory.
dc.descriptionSome errors and misprints corrected; new references have been added
dc.identifierhttps://arxiv.org/abs/math/0504603
dc.identifierhttp://arxiv.org/abs/math/0504603
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75050
dc.subjectProbability
dc.subjectClassical Analysis and ODEs
dc.subject60F-xx; 43A35
dc.titleSchoenberg's Theorem via the law of large numbers
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