Let $f(q)$ be a function over the real numbers us and consider the shift operator of Quantum mechanics: $\operatorname{Sh}_a$ which upon acting on $f(q)$, gives us its shifted value: $\operatorname{Sh}_a(f)(q) = f(q + a)$, with $a>0$ a given positive number.
It is known that $\operatorname{Sh}(f)$ can be written in the operator form: $\operatorname{Sh}_a(f)(q) = e^{a D}(f)$, where $D = \frac{\mathrm{d}}{\mathrm{d}q}$ is the derivative operator with respect to the variable $q$. Let us further consider another given function of $q$: $\lambda_2(q)$.
My question is: Is it possible to write the new operator $(1 - \lambda_2(q)e^{a D})$ in matrix form?