Let $f(z)$ be an entire function such that $\vert f(z)\vert \leq K e^{\gamma \vert z\vert}$ for some $K \geq 0$ and $\gamma > 0$ If the restriction of $f$ to the real line is in $L^2(\mathbb{R})$ then there exists a function $g(t)\in L^2(-\gamma, \gamma)$ such that $$ f(z) = \frac{1}{\sqrt{2\pi}}\int_{-\gamma}^{\gamma}g(t)e^{izt}dt$$ for all $z$