= Canonical factorization of a rational scalar Riemann-Hilbert jump
{title2=$G=X_+/X_-$}
A rational jump with no zeros or poles on the contour can be split into factors analytic and nonvanishing on the two sides. The exterior factor may carry a power of $z$ recording the winding number. For a circle enclosing $0,\pm1$, the jump $G=z/(z^2-1)$ has the canonical factors $X_+=1$, $X_-=z-z^{-1}$. The exterior growth of $X_-$ imposes compatibility conditions when a Cauchy transform is required to vanish at infinity.
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