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arXiv · 2002.12698

Fourier analysis with generalized integration

Juan H. Arredondo·M. Guadalupe Morales·Manuel Bernal G
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Abstract

We generalize the classic Fourier transform operator $\mathcal{F}_{p}$ by using the Henstock-Kurzweil integral theory. It is shown that the operator equals the $HK$-Fourier transform on a dense subspace of $\mathcal{ L}^p$, $1<p\leq 2$. 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 $\mathcal{F}_{p}(f)$ under more general conditions than in Lebesgue's theory.

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BibTeXRIS

Juan H. Arredondo, M. Guadalupe Morales, Manuel Bernal G. 2020-02-28. Fourier analysis with generalized integration. https://doi.org/10.3390/math8071199

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