= Dispersion symmetry elimination of a boundary trace
{title2=$\omega(\nu(k))=\omega(k)$}
To eliminate an unknown boundary transform by a <dispersion relation> symmetry, evaluate the <global relation> at $\nu(k)$ only where the spatial transform remains analytic. Substitute the resulting trace identity into the contour representation. An unwanted transform vanishes only if its transformed argument and exponential admit a valid <contour deformation> and decay estimate. For constant drift, $\nu(k)=i\alpha-k$ maps the upper domain $\operatorname{Re}(k^2-i\alpha k)<0$ into the lower transform half-plane.
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