HERGLOTZ-BOCHNER REPRESENTATION THEOREM VIA THEORY OF DISTRIBUTIONS

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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Bibliographic Details
Published inJournal of the Operations Research Society of Japan Vol. 60; no. 2; pp. 122 - 135
Main Author Maruyama, Toru
Format Journal Article
LanguageEnglish
Published Tokyo The Operations Research Society of Japan 2017
Nihon Opereshonzu Risachi Gakkai, Operations Research Society of Japan
Subjects
Applied probability
Fourier transform of measures
Fourier transforms
Operations research
periodic distribution
positive semi-definite
Radon
Studies
tempered distribution
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Summary: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.
ISSN:0453-4514
2188-8299
1878-6871
DOI:10.15807/jorsj.60.122