Definition:Inverse Fourier Transform/Real Function/Formulation 1

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

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

Also see

 * Conversion between Formulations of Real Fourier Transforms