Henstock--Kurzweil Fourier transforms

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dc.creatorTalvila, Erik
dc.date2002-12-07
dc.date.accessioned2026-07-07T04:53:36Z
dc.date.available2026-07-07T04:53:36Z
dc.descriptionThe Fourier transform is considered as a Henstock--Kurzweil integral. Sufficient conditions are given for the existence of the Fourier transform and necessary and sufficient conditions are given for it to be continuous. The Riemann--Lebesgue lemma fails: Henstock--Kurzweil Fourier transforms can have arbitrarily large point-wise growth. Convolution and inversion theorems are established. An appendix gives sufficient conditions for interchanging repeated Henstock--Kurzweil integrals and gives an estimate on the integral of a product.
dc.descriptionTo appear in Illinois Journal of Mathematics
dc.identifierhttps://arxiv.org/abs/math/0212105
dc.identifierhttp://arxiv.org/abs/math/0212105
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65917
dc.subjectClassical Analysis and ODEs
dc.subject42A38, 26A39
dc.titleHenstock--Kurzweil Fourier transforms
dc.typetext

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