We know that the roots of a complex polynomial are a continuous function of the coefficients of the polynomial. (See for example this stackexchange post for a discussion.)
Is there a similar continuity for the factorization of a differential operator?
I.e., given a given differential operator like, for example, $$ \mathcal D = \partial^2 + A(x) \partial + B(x), $$ where $\partial$ is shorthand for $\frac{\mathrm d}{\mathrm dx}$, do there exist functions $C(x)$ and $D(x)$ which are (in some appropriate sense) continuously dependent on $A(x)$ and $B(x)$ and such that $$ \mathcal D = (\partial + C(x))(\partial + D(x)) \quad \textrm{?} $$
