An algebraic approach to tempered distributions (Q719562)

The space \(S'(\mathbb{R}^N)\) of tempered distributions is shown to be isomorphic to a space \(B= B(M,G)\) of pseudoquotients. The Fourier transform of \(F\in B\) is defined as \(\widehat F: B\to S'\). The inverse Fourier transform is proved to be a continuous mapping from \(S'\) to \(B\).