Henstock--Kurzweil Fourier transforms

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The 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.
To appear in Illinois Journal of Mathematics

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Classical Analysis and ODEs, 42A38, 26A39

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http://salesiana.dossiersoluciones.com/handle/123456789/65917

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0212105
 http://arxiv.org/abs/math/0212105

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arXiv