Talk:Fourier transformation

MishMash

The Fourier transformation (often called the "Fourier transform" or "Fourier integral") is an invertible integral transformation that decomposes a square integrable, piecewise continuous functions on a topological group into a linear combination of basis elements.

1. Shouldn't we start with classes of functions on $\mathbf {C} ^{n}$? Test functions ${\mathcal {D}}$? And then perhaps tempered distributions ${\mathcal {S}}$?
2. What's the "piecewise continuous" part about?
3. Yes, it can be done on a locally compact abelian group, but just to throw in half of the necessary conditions isn't helpful, IMO

I'd like to rewrite the article as stated above... Any objections? --DiEb 11:14, 22 August 2008 (EDT)