Self-adjointness and Domain of the Nelson Hamiltonian

It is well-known that the Nelson Hamiltonian can be realized as norm-resolvent limit of operators where an ultraviolet cutoff is imposed  and after subtracting a suitable renormalization constant. From the  usual computations, one obtains only an abstract existence statement  about the operator. In the talk, I want to present some properties of  the domain of the renormalized Nelson Hamiltonian that can be obtained,  nevertheless.