  I consider general reflection coefficients for arbitrary one-dimensional
whole line differential or difference operators of order $2$. These reflection
coefficients are semicontinuous functions of the operator: their absolute value
can only go down when limits are taken. This implies a corresponding
semicontinuity result for the absolutely continuous spectrum, which applies to
a very large class of maps. In particular, we can consider shift maps (thus
recovering and generalizing a result of Last-Simon) and flows of the Toda and
KdV hierarchies (this is new). Finally, I evaluate an attempt at finding a
similar general setup that gives the much stronger conclusion of reflectionless
limit operators in more specialized situations.
