A new way to extend the Fourier transform to spaces $\ L^{p}(\mathbb{R})$

Ponente(s): Francisco Javier Mendoza Torres, Juan Alberto Escamilla Reyna, Germán Antonio Vázquez Romero

The usual way to define the Fourier transform on $\ L^{2}(\mathbb{R})$ has been through of dense subspaces $D\left( \mathbb{R}\right) $ in $L^{2}( \mathbb{R})$ that are at the same time are contained in $L^{1}\left( \mathbb{R}\right) .$In this article we prove that the extension of the Fourier transform on $L^{2}(\mathbb{R}),$ and as a consequence the $L^{p}(\mathbb{R})$, $1