Fourier analysis with generalized integration
Classical Analysis and ODEs
2020-07-23 v1
Abstract
We generalize the classic Fourier transform operator by using the Henstock-Kurzweil integral theory. It is shown that the operator equals the -Fourier transform on a dense subspace of , . In particular, a theoretical scope of this representation is raised to approximate numerically the Fourier transform of functions on the mentioned subspace. Besides, we show differentiability of the Fourier transform function under more general conditions than in Lebesgue's theory.
Cite
@article{arxiv.2002.12698,
title = {Fourier analysis with generalized integration},
author = {Juan H. Arredondo and M. Guadalupe Morales and Manuel Bernal G},
journal= {arXiv preprint arXiv:2002.12698},
year = {2020}
}