Definition:Inverse Fourier Transform/Real Function/Formulation 3

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:
 * $\ds \map \FF {\map F s} := \map f t = \dfrac 1 {\sqrt {2 \pi} } \int_{-\infty}^\infty e^{i t s} \map F s \rd s$

Also see

 * Conversion between Formulations of Real Fourier Transforms