Consider the propagator obtained by the replacement (omega^{2} ightarrow omega^{2}+i epsilon) (anti-Feynman) in the Fourier transform.

Consider the propagator obtained by the replacement \(\omega^{2} \rightarrow \omega^{2}+i \epsilon\) ("anti-Feynman") in the Fourier transform. Calculate the integral, and find the corresponding boundary conditions for the (Hilbert space of) functions over which we invert the kinetic operator.