I used to write on douban for the previous two months, but as there lack the support for tex and other things, I would return to this place and record more academic stuff here. This is what I learnt today.
1. In mathematics, Schwartz space is the function space of functions all of whose derivatives are rapidly decreasing. This space has the important property that the Fourier transform is an automorphism on this space. This property enables one, by duality, to define the Fourier transform for elements in the dual space of S, that is, for tempered distributions.