How do I know that a tempered distribution supported on $\mathbb{R}_+$ has a holomorphic Fourier transform on the upper half plane?

Question

I have ran into the result described in the title quite frequently. But I cannot find the exact theorem that yields the result.

Could anyone tell me what kind of theorem it is?:

A tempered distribution supported on the positive semi-axis has the Fourier transform which is a holomorphic function on the upper half plane.