Definition 12.4.1 (Fourier Transform).label Let $f\in L^{1}(\R^{n})$ then the Fourier transform of $f$ is
\begin{align*}\ha{f}(\xi)\define \integral{\R^n}{}e^{-2\pi ix\cd\xi}f(x)dx\end{align*}
for $x,\xi\in\R^{n}$. The Fourier transform is bounded since $\norm{\ha{f}}{\infty}\leq\norm{f}{1}$.
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