Henstock--Kurzweil Fourier transforms
Classical Analysis and ODEs
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0212105,
title = {Henstock--Kurzweil Fourier transforms},
author = {Erik Talvila},
journal= {arXiv preprint arXiv:math/0212105},
year = {2007}
}
Comments
To appear in Illinois Journal of Mathematics