We introduce some spaces of generalized functions that are defined as generalized quotients and Boehmians. The spaces provide simple and natural frameworks for extensions of the Fourier transform.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm108-2-8, author = {Dragu Atanasiu and Piotr Mikusi\'nski}, title = {On the Fourier transform, Boehmians, and distributions}, journal = {Colloquium Mathematicae}, volume = {107}, year = {2007}, pages = {263-276}, zbl = {1274.42018}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm108-2-8} }
Dragu Atanasiu; Piotr Mikusiński. On the Fourier transform, Boehmians, and distributions. Colloquium Mathematicae, Tome 107 (2007) pp. 263-276. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm108-2-8/