Definition:Fourier Transform of Tempered Distribution

Definition
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.