= Half-line NLS spectral functions
{title2=$s=\begin{pmatrix}a^\sharp&b\\b^\sharp&a\end{pmatrix},\quad S=\begin{pmatrix}A^\sharp&B\\B^\sharp&A\end{pmatrix}$}
Initial scattering gives $s$ and boundary-time scattering gives $S$. The defocusing reduction and unit determinants give the displayed matrix forms. The initial functions $a,b$ are analytic in the upper half-plane, while the boundary functions $A,B$ are bounded in the first and third quadrants. Their finite-horizon compatibility is the <half-line NLS global relation>.
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