  In the large polaron model of H. Froehlich, the electron-phonon interaction
is a small perturbation in form sense, but a large perturbation in operator
sense. This means that the form-domain of the Hamiltonian is not affected by
the interaction but the domain of self-adjointness is. In the particular case
of the Froehlich model, we are nevertheless able, thanks to a recently
published new operator bound, to give an explicit characterization of the
domain in terms of a suitable dressing transform. Using the mapping properties
of this dressing transform, we analyze the smoothness of vectors in the domain
of the Hamiltonian with respect to the position of the electron.
