Definition:Fourier Transform/Real Function/Formulation 1

Definition
Let $f: \R \to \R$ be a real function which is Lebesgue integrable.

The Fourier transform of $f$ is defined and denoted as:
 * $\ds \map \FF {\map f t} = \map {\hat f} s := \int_{-\infty}^\infty e^{-2 \pi i s t} \map f t \rd t$

Also see

 * Conversion between Formulations of Real Fourier Transforms