Journal of the Operations Research Society of Japan
Online ISSN : 2188-8299
Print ISSN : 0453-4514
ISSN-L : 0453-4514
HERGLOTZ-BOCHNER REPRESENTATION THEOREM VIA THEORY OF DISTRIBUTIONS
Toru Maruyama
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Keywords: Applied probability, periodic distribution, positive semi-definite, tempered distribution, Fourier transform of measures
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2017 Volume 60 Issue 2 Pages 122-135

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Abstract

Any positive semi-definite function defined on Z (resp. R) can be represented as the Fourier transform of a positive Radon measure on T (resp. R). We give a proof of this celebrated result due to Herglotz and Bochner from the viewpoint of Schwartz's theory of distributions.

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© 2017 The Operations Research Society of Japan
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