Evaluated imaginary part and its support

Thus observation-spacelike pairs can have nonzero imaginary part. The relevant spacelike region is the region between the two cones, not the region beyond the reflected cone.

Two checks follow directly from the Fourier identity. The functions $H$ and $D$ are respectively even and odd in $v$. At $t=0$, the locked kernel vanishes and (eq:imag-decomposition) gives zero because $H(-s)=H(s)$. At $s=0$, the two cosine terms cancel and

These are identities in the spatial distribution variable, not assignments of pointwise cone values.