= Dirichlet spectral formula for half-line constant drift
{c}
{title2=$q=I_{\mathbb R}[Q]-I_L[Q(i\alpha-k)+(2ik+\alpha)G_0]$}
Let $I_C[F]=(2\pi)^{-1}\int_Ce^{ikx-(k^2-i\alpha k)t}F(k)dk$. The <drift-diffusion half-line global relation> and the <half-line drift null contour identity> give the formula in the secondary title. Its real-space kernel is the difference of two drifted <Gaussian heat kernels>, and its boundary-forcing kernel is $x(2\sqrt\pi t^{3/2})^{-1}\exp[-(x+\alpha t)^2/(4t)]$. This kernel is an <approximate identity> in time as $x\downarrow0$, which verifies the <Dirichlet boundary condition>.
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