Erik Talvila

collaborators

3 papers

math.CA2026

Fourier transforms of bounded functions

Erik Talvila

The Fourier transform of a bounded measurable function, $f$ , on the real line is shown to be the second distributional derivative of a HÃ¶lder continuous function. The Fourier tran…

math.CA2025

The Fourier transform in Lebesgue spaces

Erik Talvila

For each $f \in L^{p} (R)$ ( $1 \leq p < \infty$ ) it is shown that the Fourier transform is the distributional derivative of a HÃ¶lder continuous function. For each $p$ a norm is…

math.CA2025

The Fourier transform with Henstock--Kurzweil and continuous primitive integrals

Erik Talvila

For each $f : R \to C$ that is Henstock--Kurzweil integrable on the real line, or is a distribution in the completion of the space of Henstock--Kurzweil integrabl…