If an entire holomorphic function $f(z)$ is given by the analytic continuation of $f(x)=\int_\mathbb{R}e^{-ix\xi}\,d\mu(\xi)$ with a finite Borel measure $\mu$ on $\mathbb{R}$, then $g(x):=\int_\mathbb{R_{\geq 0 }}e^{-ix\xi}\,d\mu(\xi)$ extends holomorphically to an entire function?