Schoenberg’s Theorem via the Law of Large Numbers
نویسنده
چکیده
A classical theorem of S. Bochner states that a function f : R → 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 converse to Bochner’s theorem. We present a non-technical derivation of of Schoenberg’s theorem that relies chiefly on the law of large numbers of classical probability theory.
منابع مشابه
Schoenberg’s Theorem via the Law of Large Numbers (not for Publication)
A classical theorem of S. Bochner states that a function f : Rn → 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 Finetti theorem and the law of large numbers of classical probability ...
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