= Semistrip Laplace spectral global relation
{title2=$e^{kl}N_l-N_0+k(G_0-e^{kl}G_l)-W-ikH=0$}
Let $q$ be a real <harmonic function> in a semistrip, $g_0(x)=q(x,0)$, $g_l(x)=q(x,l)$ and $h(y)=q(0,y)$. Let $G_j,N_j$ be the negative-exponential <Half-range Fourier transforms> of $g_j$ and $q_y(x,j)$, and put $H(k)=\int_0^l e^{ky}h(y)\,dy$, $W(k)=\int_0^l e^{ky}q_x(0,y)\,dy$. The <closed differential form> $e^{-ikz}q_z\,dz$ has zero boundary integral. <Integration by parts> of tangential derivatives cancels all corner values and gives the displayed <global relation>, for $\operatorname{Im}k\leq0$.
// Target: analysis.bigb
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