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Article: A probabilistic proof for Fourier inversion formula

TitleA probabilistic proof for Fourier inversion formula
Authors
KeywordsFourier transform
Gamma distribution
Harmonic analysis
Law of large numbers
Saddle-point approximation
Solid angle
Issue Date2018
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/stapro
Citation
Statistics & Probability Letters, 2018, v. 141, p. 135-142 How to Cite?
AbstractThe celebrated Fourier inversion formula provides a useful way to re-construct a regular enough, e.g. square-integrable, function via its own Fourier transform. In this article, we give the first probabilistic proof of this classical theorem, even for Euclidean spaces of arbitrary dimension. Particularly, our proof motivates why the one-half weight, for the one-dimensional case in Lemma 1, comes naturally to play due to the inherent spatial symmetry; another similar interpretation can be found in the higher dimensional analogue.
Persistent Identifierhttp://hdl.handle.net/10722/264176
ISSN
2023 Impact Factor: 0.9
2023 SCImago Journal Rankings: 0.448
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorWong, TK-
dc.contributor.authorYam, SCP-
dc.date.accessioned2018-10-22T07:50:46Z-
dc.date.available2018-10-22T07:50:46Z-
dc.date.issued2018-
dc.identifier.citationStatistics & Probability Letters, 2018, v. 141, p. 135-142-
dc.identifier.issn0167-7152-
dc.identifier.urihttp://hdl.handle.net/10722/264176-
dc.description.abstractThe celebrated Fourier inversion formula provides a useful way to re-construct a regular enough, e.g. square-integrable, function via its own Fourier transform. In this article, we give the first probabilistic proof of this classical theorem, even for Euclidean spaces of arbitrary dimension. Particularly, our proof motivates why the one-half weight, for the one-dimensional case in Lemma 1, comes naturally to play due to the inherent spatial symmetry; another similar interpretation can be found in the higher dimensional analogue.-
dc.languageeng-
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/stapro-
dc.relation.ispartofStatistics & Probability Letters-
dc.subjectFourier transform-
dc.subjectGamma distribution-
dc.subjectHarmonic analysis-
dc.subjectLaw of large numbers-
dc.subjectSaddle-point approximation-
dc.subjectSolid angle-
dc.titleA probabilistic proof for Fourier inversion formula-
dc.typeArticle-
dc.identifier.emailWong, TK: takkwong@hku.hk-
dc.identifier.authorityWong, TK=rp02167-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.spl.2018.05.028-
dc.identifier.scopuseid_2-s2.0-85049317494-
dc.identifier.hkuros293839-
dc.identifier.volume141-
dc.identifier.spage135-
dc.identifier.epage142-
dc.identifier.isiWOS:000440961600019-
dc.publisher.placeNetherlands-
dc.identifier.issnl0167-7152-

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