\begin{definition}[Definition:Fourier Transform of Tempered Distribution]
Let $T \in \map {\SS'} \R$ be a tempered distribution.
Let $\phi \in \map \SS \R$ be a Schwartz test function.
The '''Fourier transform of tempered distribution''' $\hat T \in \map {\SS'} \R$ is defined by:
:$\map {\hat T} \phi := \map T {\hat \phi}$
where the hat denotes the Fourier transform.
\end{definition}