  In the scalar case, the spectral factorization mapping $f\to f^+$ puts a
nonnegative integrable function $f$ having an integrable logarithm in
correspondence with an outer analytic function $f^+$ such that $f = |f^+|^2$
almost everywhere. The main question addressed here is to what extent $\|f^+ -
g^+\|_{H_2}$ is controlled by $\|f-g\|_{L_1}$ and $\|\log f - \log g\|_{L_1}$.
